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Course: Numerical Methods

GAUSSIAN ELIMINATION

 

Gaussian Elimination with Partial Pivoting : Theory

 

By Autar Kaw

TOPIC DESCRIPTION
 

Learn how Gaussian elimination with partial pivoting works. Be sure to learn how Naive Gauss elimination works before you venture into this topic.

 

This video teaches you the theory behind how Gaussian elimination with partial pivoting is used to solve a set of simultaneous linear equations.
ALL VIDEOS FOR THIS TOPIC
 

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

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

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

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

 

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

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

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

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

 

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

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

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

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

 

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

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

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

 

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

Determinant of a Matrix Using Forward Elimination Method: Example [YOUTUBE 10:07]
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: UnCreative Commons Licenseiversity of South Florida, 4202 E Fowler Ave, Tampa, FL 33620-5350. All Rights Reserved. Questions, suggestions or comments, contact kaw@eng.usf.edu  This material is based upon work supported by the National Science Foundation under Grant# 0126793, 0341468, 0717624,  0836981.  Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.  Other sponsors include Maple, MathCAD, USF, FAMU and MSOE.  Numerical Methods for Undergraduates by http://numericalmethods.eng.usf.edu is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 United States License.  Based on a work at numericalmethods.eng.usf.edu.