Jacobi Iteration Method is Used in Numerical Analysis. This slide helps you to figure out the use of the Jacobi Iteration Method to submit your presentatio9n slide for academic use.
Here we focuses on Fixed-Point Iterative Technique for solving nonlinear Equations in Numerical Analysis. It is one of the opened-iterative techniques for finding roots called Fixed-Point of Non-linear Equations.
Here we have included details about relaxation method and some examples .
Contribution - Parinda Rajapakha, Hashan Wanniarachchi, Sameera Horawalawithana, Thilina Gamalath, Samudra Herath and Pavithri Fernando.
Secant method is mathematical Root finding method. Most of techniques like this method but it is useful and time managing strategy.
So, refer this method its is useful for root finding.
Episode 50 : Simulation Problem Solution Approaches Convergence Techniques S...SAJJAD KHUDHUR ABBAS
Episode 50 : Simulation Problem Solution Approaches Convergence Techniques Simulation Strategies
3.2.3.3. Quasi-Newton (QN) Methods
These methods represent a very important class of techniques because of their extensive use in practical alqorithms. They attempt to use an approximation to the Jacobian and then update this at each step thus reducing the overall computational work.
The QN method uses an approximation Hk to the true Jacobian i and computes the step via a Newton-like iteration. That is,
SAJJAD KHUDHUR ABBAS
Ceo , Founder & Head of SHacademy
Chemical Engineering , Al-Muthanna University, Iraq
Oil & Gas Safety and Health Professional – OSHACADEMY
Trainer of Trainers (TOT) - Canadian Center of Human
Development
Here we focuses on Fixed-Point Iterative Technique for solving nonlinear Equations in Numerical Analysis. It is one of the opened-iterative techniques for finding roots called Fixed-Point of Non-linear Equations.
Here we have included details about relaxation method and some examples .
Contribution - Parinda Rajapakha, Hashan Wanniarachchi, Sameera Horawalawithana, Thilina Gamalath, Samudra Herath and Pavithri Fernando.
Secant method is mathematical Root finding method. Most of techniques like this method but it is useful and time managing strategy.
So, refer this method its is useful for root finding.
Episode 50 : Simulation Problem Solution Approaches Convergence Techniques S...SAJJAD KHUDHUR ABBAS
Episode 50 : Simulation Problem Solution Approaches Convergence Techniques Simulation Strategies
3.2.3.3. Quasi-Newton (QN) Methods
These methods represent a very important class of techniques because of their extensive use in practical alqorithms. They attempt to use an approximation to the Jacobian and then update this at each step thus reducing the overall computational work.
The QN method uses an approximation Hk to the true Jacobian i and computes the step via a Newton-like iteration. That is,
SAJJAD KHUDHUR ABBAS
Ceo , Founder & Head of SHacademy
Chemical Engineering , Al-Muthanna University, Iraq
Oil & Gas Safety and Health Professional – OSHACADEMY
Trainer of Trainers (TOT) - Canadian Center of Human
Development
Research Inventy : International Journal of Engineering and Scienceresearchinventy
Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
Linear regression [Theory and Application (In physics point of view) using py...ANIRBANMAJUMDAR18
Machine-learning models are behind many recent technological advances, including high-accuracy translations of the text and self-driving cars. They are also increasingly used by researchers to help in solving physics problems, like Finding new phases of matter, Detecting interesting outliers
in data from high-energy physics experiments, Founding astronomical objects are known as gravitational lenses in maps of the night sky etc. The rudimentary algorithm that every Machine Learning enthusiast starts with is a linear regression algorithm. In statistics, linear regression is a linear approach to modelling the relationship between a scalar response (or dependent variable) and one or more explanatory variables (or independent
variables). Linear regression analysis (least squares) is used in a physics lab to prepare the computer-aided report and to fit data. In this article, the application is made to experiment: 'DETERMINATION OF DIELECTRIC CONSTANT OF NON-CONDUCTING LIQUIDS'. The entire computation is made through Python 3.6 programming language in this article.
Computer Graphics in Java and Scala - Part 1Philip Schwarz
Computer Graphics in Java and Scala - Part 1.
Continuous (Logical) and Discrete (Device) Coordinates,
with a simple yet pleasing example involving concentric triangles.
Scala code: https://github.com/philipschwarz/computer-graphics-50-triangles-scala
Errata:
1. Scala classes TrianglesPanel and Triangles need not be classes, they could just be objects.
Engineering Research Publication
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Gauss jordan and Guass elimination methodMeet Nayak
This ppt is based on engineering maths.
the topis is Gauss jordan and gauss elimination method.
This ppt having one example of both method and having algorithm.
Exact Quasi-Classical Asymptoticbeyond Maslov Canonical Operator and Quantum ...ijrap
Exact quasi-classical asymptotic beyondWKB-theory and beyondMaslov canonical operatorto
theColombeau solutions of the-dimensional Schrodinger equationis presented. Quantum jumps nature is
considered successfully. We pointed out that an explanation ofquantum jumps can be found to result from
Colombeausolutions of the Schrödinger equation alone without additional postulates.
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Our project explains about the student management. This project mainly explains the various actions related to student details. This project shows some ease in adding, editing and deleting the student details. It also provides a less time consuming process for viewing, adding, editing and deleting the marks of the students.
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Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
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Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
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Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...Dr.Costas Sachpazis
Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
1. NORTH WESTERN UNIVERSITY
Computer Science & Engineering
Course Titel: Numerical Analysis
Course Code: CSE-2321
Presentation on: Jacobi Iteration Method
Submitted by:
Name : MD. MONIRUL ISLAM
ID: 20151116010
Submitted to:
Name : SONIYA YEASMIN
Lecturer
Computer Science & Engineering
North Western University , Khulna
2. * General Introduction of Jacobi Iteration Method.
* Basic idea of Jacobi Iteration Method.
* Numerical algorithm of Jacobi Iteration Method.
* Implementation of Jacobi Iteration Method in C Programming.
* Advantages of Jacobi Iteration Method.
* Limitations of Jacobi Iteration Method.
* References.
INDEX
3. General Introduction of Jacobi Iteration Method
Jacobi iterative method is considered as an iterative algorithm which is used for
determining the solutions for the system of linear equations in numerical linear algebra,
which is diagonally dominant.
In this method, an approximate value is filled in for each diagonal element. Until it
converges, the process is iterated. This algorithm was first called the Jacobi
transformation process of matrix diagonalization.
The Jacobi iteration is the simplest of the classical iterative methods and, generally, the
slowest. However, it forms a basis for the understanding of other methods, such as
Gauss-Seidel and SOR.
4. Basic idea of Jacobi Iteration Method
Two assumptions made on Jacobi Method:
1.The system given by
a11x1 +a12x2+… a1nxn=b 1
a21x1 +a22x2+… a2nxn=b 2
an1x1 +an2x2+… annxn =b n
Has a unique solution.
2.The coefficient matrix A has no zeros on its main diagonal, namely a11, a22,ann are nonzeros.
Main idea of Jacobi method :
To begin, solve the 1st equation for x1, the 2nd equation for x2 and so on to obtain the rewritten equations:
5. Then make an initial guess of the solution . Substitute these values into the right hand side the
of the rewritten equations to obtain the first approximation,
This accomplishes one iteration.
In the same way, the second approximation is computed by substituting the first approximation’s -
vales into the right hand side of the rewritten equations.
By repeated iterations, we form a sequence of approximations .
The Jacobi Method.
For each k ≤ 1, generate the components xi
(k) of x(k) from x(k-1) by,
6. Example: Apply the Jacobi method to solve,
Continue iterations until two successive approximations are identical when rounded to three significant digits.
Solution :To begin, rewrite the system
Choose the initial guess x1=0, x2=0 and x3=0 .
The first approximation is ,
7. Continue iteration, we obtain ,
The Jacobi Method in Matrix Form
x1
Consider to solve an n×n size system of linear equations Ax=b with A= for x= [x2]
xn
We split A into,
Ax=b is transformed into (D-L-U)x = b .
Dx=(L+U)x + b.
Assume D-1 exist and D-1=
8. Then, x=D-1(L+U)x +D-1b.
The matrix form of Jacobi iterative method is ,
x(k) =D -1(L+U)x(k-1) +D -1 b k=1,2,3….
Define T=D-1(L+U) and c= D-1b Jacobi iteration method can also be written as ,
x(k) =Tx(k-1) +c k=1,2,3….
9. Numerical algorithm of Jacobi Iteration Method
Input: A=[aij] , b×XO= x0 , tolerance TOL, maximum number of iterations N.
Step 1: Set K=1
Step 2: While (k ≤ N) do step 3-6.
Step 3: For for i= 1,2,…n .
Step 4: If │ |x-X0| │< TOT Then OUTPUT (x1,x2,x3,..xn) ;
Step 5: Set k=k+1.
Step 6: For for i = 1,2,….n
Set XOi= xi
Step 7: OUTPUT (x1,x2,x3,…xn);
STOP
Another stopping criterion in Step 4:
12. Advantages of Jacobi Iteration Method
Here are some advantages of Jacobi Iteration Method
1. It is simple and numerically robust.
2. Each iterations quite fast.
3. It is highly desirable for many applications.
4. The Jacobi method first generate inexact result and subsequently refines its result at
each iteration , with the residuals Converging at an exponential rate.
13. Limitations of Jacobi Iteration Method
Here are some Limitations of Jacobi Iteration Method
1. Inflexible
The Jacobi method only works on matrices A for which p(A) < I, or ||A|| < 1holds.
This makes it inapplicable to a large set of problems.
2. Large Set-Up Time
The Jacobi method cannot immediately begin producing results.
Before it can begin its iteration, a matrix —13-1(L+U) must be computed. For large
input matrices, this may not be a trivial operation, as it takes 0(n2) time to perform this
matrix multiplication. The result is a significant lag before any results can be output.
3. It might require many iterations.
4. If the linear system is ill-conditioned, it is most probably that the Jacobi method will fail
to converge.