INTRODUCTION TO MATRIX ALGEBRA

Transforming Matrix Algebra for the STEM Undergraduate

  
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GAUSSIAN ELIMINATION (CHAPTER 06)

 

Gauss Elimination with Partial Pivoting : Round of Error : Example : Part 3 of 3

 

By Autar Kaw

TOPIC DESCRIPTION
 

Learn via an example how Gaussian elimination with partial pivoting reduces round of error. In this Part 3 of 3 back substitution steps are taken.

 

This video teaches you how error could be reduced by using Gaussian elimination with partial pivoting method with an example.
ALL VIDEOS FOR THIS TOPIC
 

Naive Gaussian elimination: Theory: Part 1 of 2 [YOUTUBE 10:27] [TRANSCRIPT]

Naive Gaussian elimination: Theory: Part 2 of 2 [YOUTUBE 2:22] [TRANSCRIPT]

Naive Gauss Elimination Method: Example: Part 1 of 2 (Forward Elimination) [YOUTUBE 10:49] [TRANSCRIPT]

Naive Gauss Elimination Method: Example: Part 2 of 2 (Back Substitution) [YOUTUBE 6:40] [TRANSCRIPT]

 

Pitfalls of Naive Gauss Elimination Method: [YOUTUBE 7:20] [TRANSCRIPT]

Naive Gauss Elimination: Round-off Error Issues: Example: Part 1 of 3 [YOUTUBE 7:20] [TRANSCRIPT]

Naive Gauss Elimination: Round-off Error Issues: Example: Part 2 of 3 [YOUTUBE 7:40] [TRANSCRIPT]

Naive Gauss Elimination: Round-off Error Issues: Example: Part 3 of 3 [YOUTUBE 8:07] [TRANSCRIPT]

 

Gaussian Elimination With Partial Pivoting: Theory [YOUTUBE 10:39] [TRANSCRIPT]

Gaussian Elimination With Partial Pivoting: Example: Part 1 of 3 (Forward Elimination) [YOUTUBE 7:15] [TRANSCRIPT]

Gaussian Elimination With Partial Pivoting: Example: Part 2 of 3 (Forward Elimination) [YOUTUBE 10:08] [TRANSCRIPT]

Gaussian Elimination With Partial Pivoting: Example: Part 3 of 3 (Back Substitution) [YOUTUBE 6:18] [TRANSCRIPT]

 

Gaussian Elimination With Partial Pivoting: Round-off Error Issues: Example: Part 1 of 3 [YOUTUBE 8:58] [TRANSCRIPT]

Gaussian Elimination With Partial Pivoting: Round-off Error Issues: Example: Part 2 of 3 [YOUTUBE 8:17] [TRANSCRIPT]

Gaussian Elimination With Partial Pivoting: Round-off Error Issues: Example: Part 3 of 3 [YOUTUBE 5:48] [TRANSCRIPT]

 

Determinant of a Matrix Using Forward Elimination Method: Background [YOUTUBE 5:17] [TRANSCRIPT]

Determinant of a Matrix Using Forward Elimination Method: Example [YOUTUBE 10:07] [TRANSCRIPT]
COMPLETE RESOURCES
  Get in one place the following: a textbook chapter, a PowerPoint presentation, individual YouTube lecture videos, worksheets to illustrate the method and its convergence, and multiple-choice questions on Gaussian Elimination.

Copyrights: University of South Florida, 4202 E Fowler Ave, Tampa, FL 33620-5350. All Rights Reserved.

Questions, suggestions or comments, contact kaw@usf.edu 

This material is based upon work supported by the National Science Foundation under Grant# 0126793, 0341468, 0717624,  0836981, 0836916, 0836805, 1322586.  Any opinions, findings, and conclusions orCreative Commons License recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.  Based on a work at http://mathforcollege.com/ma.  Introduction to Matrix Algebra is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.