### Highlights from Gauss-Jordan Elimination with Partial Pivoting

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# Gauss-Jordan Elimination with Partial Pivoting

### Miguel D. B. (view profile)

10 Mar 2006 (Updated )

Gauss-Jordan Elimination with Partial Pivoting

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Description

This file contains a function named "elimgauss03" which computes the reduced row echelon form of a matrix using gauss-jordan elimination with partial pivoting. As an attempt to minimize the number of calculations needed, the algorithm does not compute some unnecessary calculations.

For example, given the matrix
A =
16 2 3 13
5 11 10 8
9 7 6 12

The program would first divide the first row by 16. However, since this is done in order to make 1 the element A(1,1), the algorithm only computes A(1,2:end)=A(1,2:end)/A(1,1), and then makes A(1,1)=1.

Similarly, once the former operation is done, we will proceed to make more row operations until the first column of the matrix turns into [1; 0; 0]. The corresponding substractions are not computed, and the instruction A(2:end,1)=0 is used instead.

Thus, we have
ยป elimgauss03(A)
ans =
Columns 1 through 3
1 0 0
0 1 0
0 0 1
Column 4
1
3
-3

MATLAB release MATLAB 5.3 (R11)
11 Feb 2012 Roengrin Shaecil

### Roengrin Shaecil (view profile)

20 Oct 2008 salman nasim

i like it

Comment only
20 Oct 2008 salman nasim
15 Feb 2008 Tim Davis

Mediocre. This can be done with a single for loop. In addition, the only purpose of this code is for educational uses, since the built-in MATLAB code is vastly superior. This code should thus be loaded with comments to describe what it does. The comments are very terse. In short, this file is rather useless and a distraction to people looking for either (a) real good code to use, or (b) real good code to read for instructional purposes.

06 Feb 2008 abalegn dagnachew

clear and simple code

10 Dec 2007 nasim abbas

it is good site

Comment only
22 Jul 2007 varin vongmanee
06 May 2007 bbb hhh

thank you for help me

18 Apr 2007 Daulet Aktan
23 Mar 2006 Duane Hanselman

This function duplicates what the MATLAB function rref already does. "R = rref(A) produces the reduced row echelon form of A using Gauss Jordan elimination with partial pivoting." There is no need to mimic a function that has been in MATLAB for 20 years.

17 Mar 2006 BIKASH SAHOO

This is very efficient code.