International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
THE LEFT AND RIGHT BLOCK POLE PLACEMENT COMPARISON STUDY: APPLICATION TO FLIG...ieijjournal
It is known that if a linear-time-invariant MIMO system described by a state space equation has a number of states divisible by the number of inputs and it can be transformed to block controller form, we can design a state feedback controller using block pole placement technique by assigning a set of desired Block poles. These may be left or right block poles. The idea is to compare both in terms of system’s response.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Scilab Finite element solver for stationary and incompressible navier-stokes ...Scilab
In this paper we show how Scilab can be used to solve Navier-stokes equations, for the incompressible and stationary planar flow. Three examples have been presented and some comparisons with reference solutions are provided.
Contradictory of the Laplacian Smoothing Transform and Linear Discriminant An...TELKOMNIKA JOURNAL
Laplacian smoothing transform uses the negative diagonal element to generate the new space. The negative diagonal elements will deliver the negative new spaces. The negative new spaces will cause decreasing of the dominant characteristics. Laplacian smoothing transform usually singular matrix, such that the matrix cannot be solved to obtain the ordered-eigenvalues and corresponding eigenvectors. In this research, we propose a modeling to generate the positive diagonal elements to obtain the positive new spaces. The secondly, we propose approach to overcome singularity matrix to found eigenvalues and eigenvectors. Firstly, the method is started to calculate contradictory of the laplacian smoothing matrix. Secondly, we calculate the new space modeling on the contradictory of the laplacian smoothing. Moreover, we calculate eigenvectors of the discriminant analysis. Fourth, we calculate the new space modeling on the discriminant analysis, select and merge features. The proposed method has been tested by using four databases, i.e. ORL, YALE, UoB, and local database (CAI-UTM). Overall, the results indicate that the proposed method can overcome two problems and deliver higher accuracy than similar methods.
Second or fourth-order finite difference operators, which one is most effective?Premier Publishers
This paper presents higher-order finite difference (FD) formulas for the spatial approximation of the time-dependent reaction-diffusion problems with a clear justification through examples, “why fourth-order FD formula is preferred to its second-order counterpart” that has been widely used in literature. As a consequence, methods for the solution of initial and boundary value PDEs, such as the method of lines (MOL), is of broad interest in science and engineering. This procedure begins with discretizing the spatial derivatives in the PDE with algebraic approximations. The key idea of MOL is to replace the spatial derivatives in the PDE with the algebraic approximations. Once this procedure is done, the spatial derivatives are no longer stated explicitly in terms of the spatial independent variables. In other words, only one independent variable is remaining, the resulting semi-discrete problem has now become a system of coupled ordinary differential equations (ODEs) in time. Thus, we can apply any integration algorithm for the initial value ODEs to compute an approximate numerical solution to the PDE. Analysis of the basic properties of these schemes such as the order of accuracy, convergence, consistency, stability and symmetry are well examined.
A Method for the Reduction 0f Linear High Order MIMO Systems Using Interlacin...IJMTST Journal
This paper presents a new mixed method for the reduction of linear high order MIMO system. This method
is based upon the interlacing property by which the denominator polynomial of the reduced order model is
obtained and the numerator is obtained by using factor division method. In general, the stability of the high
order system is retained in their models. Better approximation of the time response characteristics is
attained by using this suggested method. The number of computations has been reduced when compared to
several of the existing methods are in international literature. Another advantage of this method is that it is a
direct method. The suggested procedure is digital computer oriented.
THE LEFT AND RIGHT BLOCK POLE PLACEMENT COMPARISON STUDY: APPLICATION TO FLIG...ieijjournal
It is known that if a linear-time-invariant MIMO system described by a state space equation has a number of states divisible by the number of inputs and it can be transformed to block controller form, we can design a state feedback controller using block pole placement technique by assigning a set of desired Block poles. These may be left or right block poles. The idea is to compare both in terms of system’s response.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Scilab Finite element solver for stationary and incompressible navier-stokes ...Scilab
In this paper we show how Scilab can be used to solve Navier-stokes equations, for the incompressible and stationary planar flow. Three examples have been presented and some comparisons with reference solutions are provided.
Contradictory of the Laplacian Smoothing Transform and Linear Discriminant An...TELKOMNIKA JOURNAL
Laplacian smoothing transform uses the negative diagonal element to generate the new space. The negative diagonal elements will deliver the negative new spaces. The negative new spaces will cause decreasing of the dominant characteristics. Laplacian smoothing transform usually singular matrix, such that the matrix cannot be solved to obtain the ordered-eigenvalues and corresponding eigenvectors. In this research, we propose a modeling to generate the positive diagonal elements to obtain the positive new spaces. The secondly, we propose approach to overcome singularity matrix to found eigenvalues and eigenvectors. Firstly, the method is started to calculate contradictory of the laplacian smoothing matrix. Secondly, we calculate the new space modeling on the contradictory of the laplacian smoothing. Moreover, we calculate eigenvectors of the discriminant analysis. Fourth, we calculate the new space modeling on the discriminant analysis, select and merge features. The proposed method has been tested by using four databases, i.e. ORL, YALE, UoB, and local database (CAI-UTM). Overall, the results indicate that the proposed method can overcome two problems and deliver higher accuracy than similar methods.
Second or fourth-order finite difference operators, which one is most effective?Premier Publishers
This paper presents higher-order finite difference (FD) formulas for the spatial approximation of the time-dependent reaction-diffusion problems with a clear justification through examples, “why fourth-order FD formula is preferred to its second-order counterpart” that has been widely used in literature. As a consequence, methods for the solution of initial and boundary value PDEs, such as the method of lines (MOL), is of broad interest in science and engineering. This procedure begins with discretizing the spatial derivatives in the PDE with algebraic approximations. The key idea of MOL is to replace the spatial derivatives in the PDE with the algebraic approximations. Once this procedure is done, the spatial derivatives are no longer stated explicitly in terms of the spatial independent variables. In other words, only one independent variable is remaining, the resulting semi-discrete problem has now become a system of coupled ordinary differential equations (ODEs) in time. Thus, we can apply any integration algorithm for the initial value ODEs to compute an approximate numerical solution to the PDE. Analysis of the basic properties of these schemes such as the order of accuracy, convergence, consistency, stability and symmetry are well examined.
A Method for the Reduction 0f Linear High Order MIMO Systems Using Interlacin...IJMTST Journal
This paper presents a new mixed method for the reduction of linear high order MIMO system. This method
is based upon the interlacing property by which the denominator polynomial of the reduced order model is
obtained and the numerator is obtained by using factor division method. In general, the stability of the high
order system is retained in their models. Better approximation of the time response characteristics is
attained by using this suggested method. The number of computations has been reduced when compared to
several of the existing methods are in international literature. Another advantage of this method is that it is a
direct method. The suggested procedure is digital computer oriented.
The Positive Effects of Fuzzy C-Means Clustering on Supervised Learning Class...Waqas Tariq
Selection of inputs is one of the most substantial components of classification algorithms for data mining and pattern recognition problems since even the best classifier will perform badly if the inputs are not selected very well. Big data and computational complexity are main cause of bad performance and low accuracy for classical classifiers. In other words, the complexity of classifier method is inversely proportional with its classification efficiency. For this purpose, two hybrid classifiers have been developed by using both type-1 and type-2 fuzzy c-means clustering with cascaded a classifier. In this proposed classifier, a large number of data points are reduced by using fuzzy c-means clustering before applied to a classifier algorithm as inputs. The aim of this study is to investigate the effect of fuzzy clustering on well-known and useful classifiers such as artificial neural networks (ANN) and support vector machines (SVM). Then the role of positive effects of these proposed algorithms were investigated on applied different data sets.
In this paper, block-oriented systems with linear parts based on Laguerre functions is used to
approximation of a cone crusher dynamics. Adaptive recursive least squares algorithm is used to
identification of Laguerre model. Various structures of Hammerstein, Wiener, Hammerstein-Wiener models
are tested and the MATLAB simulation results are compared. The mean square error is used for models
validation.It has been found that Hammerstein-Wiener with orthonormal basis functions improves the
quality of approximation plant dynamics. The mean square error for this model is 11% on average
throughout the considered range of the external disturbances amplitude. The analysis also showed that
Wiener model cannot provide sufficient approximation accuracy of the cone crusher dynamics. During the
process it is unstable due to the high sensitivity to disturbances on the output.The Hammerstein-Wiener
model will be used to the design nonlinear model predictive control application.
Scalability has been an essential factor for any kind of computational algorithm while considering its performance. In this Big Data era, gathering of large amounts of data is becoming easy. Data analysis on Big Data is not feasible using the existing Machine Learning (ML) algorithms and it perceives them to perform poorly. This is due to the fact that the computational logic for these algorithms is previously designed in sequential way. MapReduce becomes the solution for handling billions of data efficiently. In this report we discuss the basic building block for the computations behind ML algorithms, two different attempts to parallelize machine learning algorithms using MapReduce and a brief description on the overhead in parallelization of ML algorithms.
Finite Element Analysis is a widely used computational method in most of the engineering domains. But still, its considered as a difficult topic by most students. This presentation is an effort to introduce the very basics of FEA so as to build an intuitive feel for the method. Enjoy !
Radial basis function neural network control for parallel spatial robotTELKOMNIKA JOURNAL
The derivation of motion equations of constrained spatial multibody system is an important problem of dynamics and control of parallel robots. The paper firstly presents an overview of the calculating the torque of the driving stages of the parallel robots using Kronecker product. The main content of this paper is to derive the inverse dynamics controllers based on the radial basis function (RBF) neural network control law for parallel robot manipulators. Finally, numerical simulation of the inverse dynamics controller for a 3-RRR delta robot manipulator is presented as an illustrative example.
Principal component analysis - application in financeIgor Hlivka
Principal component analysis is a useful multivariate times series method to examine and study the drivers of the changes in the entire dataset. The main advantage of PCA is the reduction of dimensionality where the large sets of data get transformed into few principal factors that explain majority of variability in that group. PCA has found many applications in finance – both in risk and yield curve analytics
The International Journal of Engineering and Science (The IJES)theijes
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
On selection of periodic kernels parameters in time series predictioncsandit
In the paper the analysis of the periodic kernels parameters is described. Periodic kernels can
be used for the prediction task, performed as the typical regression problem. On the basis of the
Periodic Kernel Estimator (PerKE) the prediction of real time series is performed. As periodic
kernels require the setting of their parameters it is necessary to analyse their influence on the
prediction quality. This paper describes an easy methodology of finding values of parameters of
periodic kernels. It is based on grid search. Two different error measures are taken into
consideration as the prediction qualities but lead to comparable results. The methodology was
tested on benchmark and real datasets and proved to give satisfactory results.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
The Positive Effects of Fuzzy C-Means Clustering on Supervised Learning Class...Waqas Tariq
Selection of inputs is one of the most substantial components of classification algorithms for data mining and pattern recognition problems since even the best classifier will perform badly if the inputs are not selected very well. Big data and computational complexity are main cause of bad performance and low accuracy for classical classifiers. In other words, the complexity of classifier method is inversely proportional with its classification efficiency. For this purpose, two hybrid classifiers have been developed by using both type-1 and type-2 fuzzy c-means clustering with cascaded a classifier. In this proposed classifier, a large number of data points are reduced by using fuzzy c-means clustering before applied to a classifier algorithm as inputs. The aim of this study is to investigate the effect of fuzzy clustering on well-known and useful classifiers such as artificial neural networks (ANN) and support vector machines (SVM). Then the role of positive effects of these proposed algorithms were investigated on applied different data sets.
In this paper, block-oriented systems with linear parts based on Laguerre functions is used to
approximation of a cone crusher dynamics. Adaptive recursive least squares algorithm is used to
identification of Laguerre model. Various structures of Hammerstein, Wiener, Hammerstein-Wiener models
are tested and the MATLAB simulation results are compared. The mean square error is used for models
validation.It has been found that Hammerstein-Wiener with orthonormal basis functions improves the
quality of approximation plant dynamics. The mean square error for this model is 11% on average
throughout the considered range of the external disturbances amplitude. The analysis also showed that
Wiener model cannot provide sufficient approximation accuracy of the cone crusher dynamics. During the
process it is unstable due to the high sensitivity to disturbances on the output.The Hammerstein-Wiener
model will be used to the design nonlinear model predictive control application.
Scalability has been an essential factor for any kind of computational algorithm while considering its performance. In this Big Data era, gathering of large amounts of data is becoming easy. Data analysis on Big Data is not feasible using the existing Machine Learning (ML) algorithms and it perceives them to perform poorly. This is due to the fact that the computational logic for these algorithms is previously designed in sequential way. MapReduce becomes the solution for handling billions of data efficiently. In this report we discuss the basic building block for the computations behind ML algorithms, two different attempts to parallelize machine learning algorithms using MapReduce and a brief description on the overhead in parallelization of ML algorithms.
Finite Element Analysis is a widely used computational method in most of the engineering domains. But still, its considered as a difficult topic by most students. This presentation is an effort to introduce the very basics of FEA so as to build an intuitive feel for the method. Enjoy !
Radial basis function neural network control for parallel spatial robotTELKOMNIKA JOURNAL
The derivation of motion equations of constrained spatial multibody system is an important problem of dynamics and control of parallel robots. The paper firstly presents an overview of the calculating the torque of the driving stages of the parallel robots using Kronecker product. The main content of this paper is to derive the inverse dynamics controllers based on the radial basis function (RBF) neural network control law for parallel robot manipulators. Finally, numerical simulation of the inverse dynamics controller for a 3-RRR delta robot manipulator is presented as an illustrative example.
Principal component analysis - application in financeIgor Hlivka
Principal component analysis is a useful multivariate times series method to examine and study the drivers of the changes in the entire dataset. The main advantage of PCA is the reduction of dimensionality where the large sets of data get transformed into few principal factors that explain majority of variability in that group. PCA has found many applications in finance – both in risk and yield curve analytics
The International Journal of Engineering and Science (The IJES)theijes
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
On selection of periodic kernels parameters in time series predictioncsandit
In the paper the analysis of the periodic kernels parameters is described. Periodic kernels can
be used for the prediction task, performed as the typical regression problem. On the basis of the
Periodic Kernel Estimator (PerKE) the prediction of real time series is performed. As periodic
kernels require the setting of their parameters it is necessary to analyse their influence on the
prediction quality. This paper describes an easy methodology of finding values of parameters of
periodic kernels. It is based on grid search. Two different error measures are taken into
consideration as the prediction qualities but lead to comparable results. The methodology was
tested on benchmark and real datasets and proved to give satisfactory results.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
AN EFFICIENT PARALLEL ALGORITHM FOR COMPUTING DETERMINANT OF NON-SQUARE MATRI...ijdpsjournal
One of the most significant challenges in Computing Determinant of Rectangular Matrices is high time
complexity of its algorithm. Among all definitions of determinant of rectangular matrices, Radic’s
definition has special features which make it more notable. But in this definition, C(N
M
) sub matrices of the
order m×m needed to be generated that put this problem in np-hard class. On the other hand, any row or
column reduction operation may hardly lead to diminish the volume of calculation. Therefore, in this paper
we try to present the parallel algorithm which can decrease the time complexity of computing the
determinant of non-square matrices to O(N
).
AN EFFICIENT PARALLEL ALGORITHM FOR COMPUTING DETERMINANT OF NON-SQUARE MATRI...ijdpsjournal
One of the most significant challenges in Computing Determinant of Rectangular Matrices is high time
complexity of its algorithm. Among all definitions of determinant of rectangular matrices, Radic’s
definition has special features which make it more notable. But in this definition, C(N
M
) sub matrices of the
order m×m needed to be generated that put this problem in np-hard class. On the other hand, any row or
column reduction operation may hardly lead to diminish the volume of calculation. Therefore, in this paper
we try to present the parallel algorithm which can decrease the time complexity of computing the
determinant of non-square matrices to O(N).
A COMPREHENSIVE ANALYSIS OF QUANTUM CLUSTERING : FINDING ALL THE POTENTIAL MI...IJDKP
Quantum clustering (QC), is a data clustering algorithm based on quantum mechanics which is
accomplished by substituting each point in a given dataset with a Gaussian. The width of the Gaussian is a
σ value, a hyper-parameter which can be manually defined and manipulated to suit the application.
Numerical methods are used to find all the minima of the quantum potential as they correspond to cluster
centers. Herein, we investigate the mathematical task of expressing and finding all the roots of the
exponential polynomial corresponding to the minima of a two-dimensional quantum potential. This is an
outstanding task because normally such expressions are impossible to solve analytically. However, we
prove that if the points are all included in a square region of size σ, there is only one minimum. This bound
is not only useful in the number of solutions to look for, by numerical means, it allows to to propose a new
numerical approach “per block”. This technique decreases the number of particles by approximating some
groups of particles to weighted particles. These findings are not only useful to the quantum clustering
problem but also for the exponential polynomials encountered in quantum chemistry, Solid-state Physics
and other applications.
A New Approach to Linear Estimation Problem in Multiuser Massive MIMO SystemsRadita Apriana
A novel approach for solving linear estimation problem in multi-user massive MIMO systems is
proposed. In this approach, the difficulty of matrix inversion is attributed to the incomplete definition of the
dot product. The general definition of dot product implies that the columns of channel matrix are always
orthogonal whereas, in practice, they may be not. If the latter information can be incorporated into dot
product, then the unknowns can be directly computed from projections without inverting the channel
matrix. By doing so, the proposed method is able to achieve an exact solution with a 25% reduction in
computational complexity as compared to the QR method. Proposed method is stable, offers an extra
flexibility of computing any single unknown, and can be implemented in just twelve lines of code.
Quantum inspired evolutionary algorithm for solving multiple travelling sales...eSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Super-resolution reconstruction is a method for reconstructing higher resolution images from a set of low resolution observations. The sub-pixel differences among different observations of the same scene allow to create higher resolution images with better quality. In the last thirty years, many methods for creating high resolution images have been proposed. However, hardware implementations of such methods are limited. Wiener filter design is one of the techniques we will use initially for this process. Wiener filter design involves matrix inversion. A novel method for the matrix inversion has been proposed in the report. QR decomposition will be the computational algorithm used using Givens Rotation.
Finite Element Analysis Lecture Notes Anna University 2013 Regulation NAVEEN UTHANDI
One of the most Simple and Interesting topics in Engineering is FEA. My work will guide average students to score good marks. I have given you full package which includes 2 Marks and Question Banks of previous year. All the Best
For Guidance : Comment Below Happy to Teach and Learn along with you guys
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
THE LEFT AND RIGHT BLOCK POLE PLACEMENT COMPARISON STUDY: APPLICATION TO FLIG...ieijjournal1
It is known that if a linear-time-invariant MIMO system described by a state space equation has a number
of states divisible by the number of inputs and it can be transformed to block controller form, we can
design a state feedback controller using block pole placement technique by assigning a set of desired Block
poles. These may be left or right block poles. The idea is to compare both in terms of system’s response.
Accelerate your Kubernetes clusters with Varnish CachingThijs Feryn
A presentation about the usage and availability of Varnish on Kubernetes. This talk explores the capabilities of Varnish caching and shows how to use the Varnish Helm chart to deploy it to Kubernetes.
This presentation was delivered at K8SUG Singapore. See https://feryn.eu/presentations/accelerate-your-kubernetes-clusters-with-varnish-caching-k8sug-singapore-28-2024 for more details.
LF Energy Webinar: Electrical Grid Modelling and Simulation Through PowSyBl -...DanBrown980551
Do you want to learn how to model and simulate an electrical network from scratch in under an hour?
Then welcome to this PowSyBl workshop, hosted by Rte, the French Transmission System Operator (TSO)!
During the webinar, you will discover the PowSyBl ecosystem as well as handle and study an electrical network through an interactive Python notebook.
PowSyBl is an open source project hosted by LF Energy, which offers a comprehensive set of features for electrical grid modelling and simulation. Among other advanced features, PowSyBl provides:
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Elevating Tactical DDD Patterns Through Object Calisthenics
N41049093
1. Monika Agarwal et al Int. Journal of Engineering Research and Applications www.ijera.com
ISSN : 2248-9622, Vol. 4, Issue 1( Version 4), January 2014, pp.90-93
www.ijera.com 90 | P a g e
Review of Matrix Decomposition Techniques for Signal
Processing Applications
Monika Agarwal*, Rajesh Mehra**
*(Department of Electronics and communication, NITTTR, Chandigarh)
** (Department of Electronics and communication, NITTTR, Chandigarh)
ABSTRACT
Decomposition of matrix is a vital part of many scientific and engineering applications. It is a technique that
breaks down a square numeric matrix into two different square matrices and is a basis for efficiently solving a
system of equations, which in turn is the basis for inverting a matrix. An inverting matrix is a part of many
important algorithms. Matrix factorizations have wide applications in numerical linear algebra, in solving linear
systems, computing inertia, and rank estimation is an important consideration. This paper presents review of all
the matrix decomposition techniques used in signal processing applications on the basis of their computational
complexity, advantages and disadvantages. Various Decomposition techniques such as LU Decomposition, QR
decomposition , Cholesky decomposition are discussed here.
Keywords – Cholesky Decomposition, LU decomposition, Matrix factorization, QR decomposition.
I. INTRODUCTION
Signal processing is an area of system
engineering, electrical engineering and applied
mathematics that deals with the operations on or
analysis of analog as well as digitized signal,
representing time varying or spatially physical
quantities. There are various mathematical model
applied in signal processing such as linear time
invariant system, system identification, optimization,
estimation theory, numerical methods [1].In the
computational application matrix decomposition is a
basic operation. “Matrix decomposition refers to the
transformation of the given matrix into a given
canonical form”. Matrix factorization is the process
of producing the decomposition where the given
matrix is transformed to right hand side product of
canonical matrices [2]. Matrix decomposition is a
fundamental theme in linear algebra and applied
statistics which has both scientific and engineering
significance. Computational convenience and
analytic simplicity are the two main aspects in the
purpose of matrix decomposition. In the real world it
is not feasible for most of the matrix computation to
be calculated in an optimal explicit way such as
matrix inversion, matrix determinant, solving linear
systems and least square fitting , thus to convert a
difficult matrix computation problem into several
easier task such as solving triangular or diagonal
systems will greatly facilitate the calculations. Data
matrices such as proximity matrix or correlation
matrix represent numerical observations and it is
often huge and hard to analyze them. Therefore to
decompose the data matrices into some lower rank
canonical forms will reveal the inherent
characteristics. Since matrix computation algorithms
are expensive computational tasks, hardware
implementation of these algorithms require
substantial time and effort. There is an increasing
demand for domain specific tool for matrix
computation algorithms which provide fast and
highly efficient hardware production. In this paper
there is review of matrix decomposition techniques
that are used in signal processing.
The paper is organized as follows: Section II
discusses the Matrix decomposition Models. Section
III concludes the paper
II. MATRIX DECOMPOSITION
MODELS
This paper discusses basically four matrix
decomposition models.
QR decomposition
SVD decomposition
LU decomposition
Cholesky Decomposition
2.1 QR decomposition
A matrix A=QR in linear algebra is a
decomposition of a matrix A into an orthogonal and
right triangular matrix. The Q-R decompositions are
generally used to solve the linear least squares
problems. If the matrix A is non-singular then the Q-
R factorization of A is a unique one if we want that
the diagonal elements of R are positive. More
generally we can factor a m x n rectangular matrix
into an m x m unitary matrix and an m x n upper
triangular matrix. There are two standard methods to
evaluate Q-R factorization of A such as Graham-
RESEARCH ARTICLE OPEN ACCESS
2. Monika Agarwal et al Int. Journal of Engineering Research and Applications www.ijera.com
ISSN : 2248-9622, Vol. 4, Issue 1( Version 4), January 2014, pp.90-93
www.ijera.com 91 | P a g e
Schmidt triangulizations and Householder
triangulizations but Householder triangulizations are
much more efficient than Graham-Schmidt
triangulizations because of the following statistics
involved. The number of operations at the kth step
are multiplications=2(n-k+1)2 , additions=(n-k+1)2 +
(n-k+1) (n-k) + 2 , division=1and square root=1.
Summing all these operations over (n-1) steps we get
the complexity as O (n3) but this involves much less
computation time than the other triangulation
methods [3]. QR factorization is an important tool for
solving linear systems of equations because of good
error propagation properties and the inevitability of
unitary matrices [4]. The main application of QR
decomposition is solving the linear least squares
problem. There exist systems of linear equations that
have no exact solutions. Linear least square is a
mathematical optimization technique used to find an
approximate solution for these systems. QR
decomposition has several advantages that it finds
least squares solution as well when no exact solution
exists, and if there is exact solution, it finds all.
2.2 SVD DECOMPOSITION
This is also one of the matrix decomposition
schemes. This is also applicable for complex
rectangular matrices of the dimensions m x n. The
singular value decomposition block factors the M-by-
N input matrix A such that [4]
A=U×diag(s)× V* (1)
Where U is an M-by-P matrix, V is an N-by-P
matrix, S is a length-P , vector P is defined as
min(M,N) When M = N, U and V are both M-by-M
unitary matrices M > N, V is an N-by-N unitary
matrix, and U is an M-by-N matrix whose columns
are the first N columns of a unitary matrix N > M, U
is an M-by-M unitary matrix, and V is an N-by-M
matrix whose columns are the first M columns of a
unitary matrix In all cases, S is a 1-D vector of
positive singular values having length P. Length-N
row inputs are treated as length-N columns. Note that
the first (maximum) element of output S is equal to
the 2-norm of the matrix A. The output is always
sampling based [4].
2.3 LU DECOMPOSITION
LU decomposition is widely used matrix
factorization algorithm. it transforms square matrix
into lower triangular matrix L and upper matrix U
with A=LU. LU decomposition used the Dolittle
algorithm for the elimination column by column from
left to right. It results in unit lower triangular matrix
that can use the storage of the original matrix A [5].
This algorithm requires 2n3/3 floating point
operations. Algorithm 1 shows the steps followed for
LU decomposition of a matrix. In each iteration , the
same steps are applied to a matrix that has one less
row and column than in the previous iteration. This
algorithms shows the parallelism of each steps while
in each iteration, a new sub matrix is constructed and
hence efficient use of local storage capacity. It would
be preferable to use an algorithm to load a block of
data into local storage performs the computation and
then transfer new block. The block LU
decomposition algorithm partitioned the entire matrix
into smaller blocks so that work can be done
concurrently to improve the performance.
Input:A- n x n matrix with elemnts a i,p
Output: L, U triangular matrices with elements l i p,
u i p
1: for p=1 : n
2. for q=1 to p-1
3. for i=q+1 to p-1
4. A[i,p]=A[i,p]- A[i, q]× A[q,p]
5. for q=1to p-1
6. for i=p to n
7. A(i,p) = A[i,p]- A[i, q]× A[q,p]
8. for q= p+1:n
9. A(q,p)=A(q,p)/A(p,p)
Algorithm 1.Basic LU decomposition
The algorithm is analyzed as it writes lower
and upper triangular matrices onto A matrices then it
updates the value of A matrix column by column ((4)
and (7)). The final values are computed by the
division of each column entry by the diagonal entry
of that column. The LU decomposition has various
advantages. it is applicable for any matrix. It can be
solved by forward substitution as well as backward
substitution. The solution of triangular set of equation
is trivial to solve. it is direct method and finds all
solution. LU decomposition is easy to program.
There are several drawbacks that it doesn’t find
approximate solution (least square). It could easily be
unstable. Hence to find the approximate solution
Cholesky decomposition is studied.
2.4 CHOLESKY DECOMPOSITION
The Cholesky decomposition factors a
positive symmetric matrix to the product of a lower
triangular matrix and its transpose, of which two
general ways are given by:
A = UT
U (2)
A = LDLT
(3)
Where A is a positive definite symmetric matrix. U is
the upper triangular matrix & UT is Transpose of
upper triangular matrix, L is the unit lower triangular
matrix & LT is lower triangular matrix and D is the
diagonal matrix in which all elements are zeros
except the diagonal elements. Cholesky
decomposition has 1/3N3 FLOPS complexity with
heavy inner data dependency. Introducing a diagonal
matrix as shown in Eq. (3) in Cholesky
3. Monika Agarwal et al Int. Journal of Engineering Research and Applications www.ijera.com
ISSN : 2248-9622, Vol. 4, Issue 1( Version 4), January 2014, pp.90-93
www.ijera.com 92 | P a g e
decomposition has many advantages, such as
avoiding square roots and alleviating data
dependency [5]. In this paper, we design and
implement the UTU Cholesky decomposition in Eq.
(2) on FPGAs for computation acceleration. Using
the fact that A is symmetric [6]:
A= LDLT
Where L is lower triangular matrix.
(4)
With Cholesky decompositions, the elements of L are
evaluated as follows:
(5)
Where k=1, 2 ….n.
(6)
Where i=1, 2…..k-1.
First subscript is row index and second one
is column index. Cholesky decomposition is
evaluated column by column and in each row the
elements are evaluated from top to bottom. That is, in
each column the diagonal element is evaluated first
using equation (4) (the elements above the diagonal
are zero) and then the other elements in the same row
are evaluated next using equation (5). This is carried
out for each column starting from the first one. Note
that if the value within the square root in equation (4)
is negative, Cholesky decomposition will fail.
However, this will not happen for positive semi
definite matrices, which are encountered commonly
in many engineering systems (e.g., circuits,
covariance matrix). Thus, Cholesky decomposition is
a good way to test for the positive semi definiteness
of symmetric matrices. A general form of the
Cholesky algorithm is given in Algorithm 2, where
the row-order representation is assumed for stored
matrices. In the above algorithm, if one changes the
order of the three for loops, one can get different
variations which give different behavior in terms of
memory access patterns and the basic linear
Algebraic operation performed in the innermost loop.
Out of the six different variations possible, only three
are of interest. They are the row-oriented, column-
oriented and sub matrixes forms and are described as:
In Row-oriented L is calculated row by row, with
the terms for each row being calculated using terms
on the preceding rows that have already been
evaluated, Column-oriented, the inner loop
computes a matrix-vector product. Here, each column
is calculated using terms from previously computed
columns. And Sub-matrix the inner loops apply the
current column as a rank-1 update to the partially
reduced sub-matrix.The algorithm is analyzed as the
decomposition by transferring the matrix A into
memory elements. The diagonal entire of lower
triangular matrix, A, are square root of diagonal
entries of given matrix (8). It calculate the entries by
dividing the corresponding element of given matrix
by the belonging column diagonal element (9) .The
algorithm works column by column and after the
computation of first column of diagonal matrix with
the given matrix entries, the elements in the next
column are updated (4).
1. For p = 1to n
2. For q=1 to j-1
3. For i = p to n
4. A[i,p] = A[i,q] – A[i,q] * A[p,q]
5 End
6 End
7 A[p,p] = √ A[p,p]
8 For q = p+1 to n
9 A[q,p]= A[q,p] / A[p,p]
10 End
11 End
Algorithm 2: General form of the Cholesky
algorithm.
In this paper, the Cholesky factorization
method has several advantages over the other
decomposition techniques. It has faster execution
because only one factor needs to be calculated as the
other factor is simply the transpose of the first one.
Thus, the number of operations for dense matrices is
approximately n3/3 under Cholesky. It is highly
adaptive to parallel architectures hence pivoting is
not required. This makes the Cholesky algorithm
especially suitable for parallel architectures as it
reduces inter-processor communications. A lot of
work [8] has been devoted to parallelizing the
Cholesky factorization method. it has significantly
lower memory requirements. In the Cholesky
algorithm, only the lower triangular matrix is used for
factorization, and the intermediate and final results
(the Cholesky factor L) are overwritten in the original
matrix. Thus, only the lower triangular matrix must
be stored, resulting in significant savings in terms of
memory requirements. it eliminates the divider
operation dependency. It improves the data
throughput.
III. CONCLUSIONS
The proposed paper review all the matrix
decomposition techniques used in signal processing
applications. QR decomposition has complicated
algorithm and also a slower algorithm. LU
decomposition doesn’t find approximate solution and
have stability issues. Cholesky decomposition can
find approximate solution of the problem. Among all
the matrix decomposition techniques Cholesky
4. Monika Agarwal et al Int. Journal of Engineering Research and Applications www.ijera.com
ISSN : 2248-9622, Vol. 4, Issue 1( Version 4), January 2014, pp.90-93
www.ijera.com 93 | P a g e
Decomposition is the well suited for signal
processing application. It is efficient in terms of
memory storage capacity, computational cost, speed,
data alleviating and throughput.
REFERENCES
[1] http://en.wikipedia.org/wiki/Signal_processi
ng
[2] E. W. Weisstein. Matrix decomposition.
MathWorld–A Wolfram Web Resource.
[Online]. Available:
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mposition.html
[3] Steven Chapra and Raymond Canale,
Numerical methods for Engineers, Fourth
Edition,Mcgraw Hill, 2002.
[4] Mathworks, “Users Guide Filter Design
Toolbox”, March-2007.
[5] R.Barett,templates for the solution of linear
systems: building blocks for iterative
method, second ed.SIAM,1994.
[6] DepengYang, G.D.Peterson, H.Li and
junquing Sun," An FPGA implementation
for solving least square problem” IEEE
Symposium on Field-Programmable Custom
Computing Machines, pp.no.306-309, 2009.
[7] X. Wang and S.G. Ziavras, "Parallel LU
Factorization of Sparse Matrices on FPGA-
Based Configurable Computing Engines,"
Concurrency and Computation: Practice and
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[8] Guiming Wu,Yong Dou,“ A High
Performance and Memory Efficient LU
decomposer on FPGAs” IEEE Transactions
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378, 2012.