Gaussian elimination is a method for solving systems of linear equations. It involves converting the augmented matrix into an upper triangular matrix using elementary row operations. There are three types of Gaussian elimination: simple elimination without pivoting, partial pivoting, and total pivoting. Partial pivoting interchanges rows to choose larger pivots, while total pivoting searches the whole matrix for the largest number to use as the pivot. Pivoting strategies help prevent zero pivots and reduce round-off errors.
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.
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.
Numerical solution of a system of linear equations by
1) LU FACTORIZATION METHOD.
2) GAUSS ELIMINATION METHOD.
3) MATRIX INVERSION BY GAUSS ELIMINATION METHOD.
This presentation will be very helpful to learn about system of linear equations, and solving the system.It includes common terms related with the lesson and using of Cramer's rule.
Please download the PPT first and then navigate through slide with mouse clicks.
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.
Numerical solution of a system of linear equations by
1) LU FACTORIZATION METHOD.
2) GAUSS ELIMINATION METHOD.
3) MATRIX INVERSION BY GAUSS ELIMINATION METHOD.
This presentation will be very helpful to learn about system of linear equations, and solving the system.It includes common terms related with the lesson and using of Cramer's rule.
Please download the PPT first and then navigate through slide with mouse clicks.
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.
Linear Systems - Expansion and Movement JointsAli Asgar Raja
LINEAR SYSTEMS is an integrated brand of various lines of building materials. Our product line includes proprietary Aluminum and Steel Expansion Joints as well as new age Foam Expansion Joints from Masterspec-USA for Buildings and infrastructure projects. Other products in our range include Stone and Tile Movement Joints, Elastomeric Concrete, PPC Coatings, Plaster Profiles, Decoration Profiles and Entrance Matting Systems. Armed with the right technical expertise, Linear Systems is a solution based brand relying on the vast experience of its core team in the local construction, application and supply markets. Based out of Dubai in the United Arab Emirates, we are poised to supply and execute projects in GCC countries including Sultanate of Oman (Muscat), Qatar (Doha), Saudi Arabia, Bahrain.
Image segmentation is a computer vision task that involves dividing an image into multiple segments or regions, where each segment corresponds to a distinct object, region, or feature within the image. The goal of image segmentation is to simplify and analyze an image by partitioning it into meaningful and semantically relevant parts. This is a crucial step in various applications, including object recognition, medical imaging, autonomous driving, and more.
Key points about image segmentation:
Semantic Segmentation: This type of segmentation assigns each pixel in an image to a specific class, essentially labeling each pixel with the object or region it belongs to. It's commonly used for object detection and scene understanding.
Instance Segmentation: Here, individual instances of objects are separated and labeled separately. This is especially useful when multiple objects of the same class are present in the image.
Boundary Detection: Some segmentation methods focus on identifying the boundaries that separate different objects or regions in an image.
Methods: Image segmentation can be achieved through various techniques, including traditional methods like thresholding, clustering, and region growing, as well as more advanced techniques involving deep learning, such as using convolutional neural networks (CNNs) and fully convolutional networks (FCNs).
Challenges: Image segmentation can be challenging due to variations in lighting, color, texture, and object shape. Overlapping objects and unclear boundaries further complicate the task.
Applications: Image segmentation is used in diverse fields. For example, in medical imaging, it helps identify organs or abnormalities. In autonomous vehicles, it aids in identifying pedestrians, other vehicles, and obstacles.
Evaluation: Measuring the accuracy of segmentation methods can be complex. Metrics like Intersection over Union (IoU) and Dice coefficient are often used to compare segmented results to ground truth.
Data Annotation: Creating ground truth annotations for segmentation can be labor-intensive, as each pixel must be labeled. This has led to the development of datasets and tools to facilitate annotation.
Semantic Segmentation Networks: Deep learning architectures like U-Net, Mask R-CNN, and Deeplab have significantly improved the accuracy of image segmentation by effectively learning complex patterns and features.
Image segmentation plays a fundamental role in understanding and processing images, enabling computers to "see" and interpret visual information in ways that mimic human perception.
Image segmentation is a computer vision task that involves dividing an image into meaningful and distinct segments or regions. The goal is to partition an image into segments that represent different objects or areas of interest within the image. Image segmentation plays a crucial role in various applications, such as object detection, medical imaging, autonomous vehicles, and more.
The assignment problem is a special case of transportation problem in which the objective is to assign ‘m’ jobs or workers to ‘n’ machines such that the cost incurred is minimized.
Introduction to Matrix Chain Multiplication algorithm with an example. Matrix Chain Products algorithm comes under Dynamic Programming concept. Done for the course Advanced Data Structures and Algorithms.
Lecture 5 - Gradient Descent, a lecture in subject module Statistical & Machi...Maninda Edirisooriya
Gradient Descent is the most commonly used learning algorithm for learning, including Deep Neural Networks with Back Propagation. This was one of the lectures of a full course I taught in University of Moratuwa, Sri Lanka on 2023 second half of the year.
3. I. Simple Elimination Without Pivoting
Let say we have a system (size 3x3)with
augmented matrix form as:
a11 a12 a13 b1
A a21 a22 a23 b2
a31 a32 a33 b3
4. Procedure to get the solution:
1. The basic idea is to convert the system of A
into upper-triangular matrix (U) form.
a11 a12 a13
U 0 a22 a23
0 0 a33
5. 2. Eliminate the element a21 and a31 using multiple
factor of
a21 and a31
m 21 m 31
a11 a11
Hence, our matrix should be like this
a11 a12 a13 b1
A 0 a22 a23 b2
0 a32 a33 b3
6. 3. Eliminate the element a32 using multiple factor
of a32 to convert A into U
m 32
a22
4. The possible diagonal element (pivot element)
should be non-zero. If it become zero at any
stage, then interchange that row with any below
row with non-zero element at that pivoting
position.
7. 5. After getting upper triangular matrix form, then
use backward substitution to get the solution of
the given linear system.
a11x 1 a12 x 2 a13x 3 b1
a22 x 2 a23x 3 b2
a33x 3 b3
8. II. Pivoting Strategies
The basic idea of pivoting strategies is;
• To prevent diagonal (pivoting) element from
becoming zero
• To make diagonal element larger in magnitude
than any other coefficient below it, that is, to
decrease round-off errors.
• After interchanging the system, use the same
procedure that we discussed to get the solution.
9. • Partial Pivoting
Interchange the largest absolute coefficient of
variable X1
Example:
Before After
2 2 2 4 2 2
4 2 2 2 2 2
2 3 9 2 3 9
10. • Total Pivoting
Search the largest number in absolute, then
interchange this as the pivot
Example:
Before After
2 2 2 9 3 2
4 2 2 2 2 4
2 3 9 2 2 2