# Gaussian Elimination - PowerPoint PPT Presentation

PPT – Gaussian Elimination PowerPoint presentation | free to download - id: 7b2d3a-NjE1Y

The Adobe Flash plugin is needed to view this content

Get the plugin now

View by Category
Title:

## Gaussian Elimination

Description:

### Holistic Numerical Methods Institute Other titles: Tahoma Arial Times New Roman Verdana Default Design Microsoft Equation 3.0 Gaussian Elimination Na ve ... – PowerPoint PPT presentation

Number of Views:91
Avg rating:3.0/5.0
Slides: 16
Provided by: Auta160
Category:
Tags:
Transcript and Presenter's Notes

Title: Gaussian Elimination

1
Gaussian Elimination
• Major All Engineering Majors
• Author(s) Autar Kaw
• http//numericalmethods.eng.usf.edu
• Transforming Numerical Methods Education for STEM

2
Naïve Gaussian Elimination
A method to solve simultaneous linear equations
of the form AXC
Two steps 1. Forward Elimination 2. Back
Substitution
3
Forward Elimination
The goal of forward elimination is to transform
the coefficient matrix into an upper triangular
matrix
4
Forward Elimination
A set of n equations and n unknowns
. . .
. . .
(n-1) steps of forward elimination
5
Forward Elimination
Step 1 For Equation 2, divide Equation 1 by
and multiply by .
6
Forward Elimination
Subtract the result from Equation 2.

- ________________________________________________
_
or
7
Forward Elimination
Repeat this procedure for the remaining equations
to reduce the set of equations as

. . .
. . .
. . .
End of Step 1
8
Forward Elimination
Step 2 Repeat the same procedure for the 3rd term
of Equation 3.

. .
. .
. .

End of Step 2
9
Forward Elimination
At the end of (n-1) Forward Elimination steps,
the system of equations will look like

. .
. .
. .

End of Step (n-1)
10
Matrix Form at End of Forward Elimination
11
Back Substitution
Solve each equation starting from the last
equation
Example of a system of 3 equations
12
Back Substitution Starting Eqns

. .
. .
. .

13
Back Substitution