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linalg_overview

An overview of the Linear Algebra toolbox.

Authors

The goal of this toolbox is to provide a collection of algorithms for linear algebra. These algorithms are most of the time already provided by Scilab, but are available here for comparison purpose.

Quick start

In the following example, factor a 2x2 matrix which requires pivoting. In the second call, we use the verbose mode.

-->A=[
-->2*%eps 1
-->1      1
-->];

-->verbose = 1;

-->[L,U,P]=linalg_factorlupivot(A,%f);

-->[L,U,P]=linalg_factorlupivot(A,%t)
=============================
Column to search for pivot : [0.00000000000000044 1]
Pivot at index 2 = 1.000000
Swap rows 2 <-> 1
Step #1 / 2
A:
    1.                     1.
    0.00000000000000044    0.99999999999999956
L:
    1.                     0.
    0.00000000000000044    1.
U:
    1.    1.
    0.    0.99999999999999956
 P  =

    0.    1.
    1.    0.
 U  =

    1.    1.
    0.    0.99999999999999956
 L  =

    1.                     0.
    0.00000000000000044    1.

Authors

Copyright (C) 2008 - 2010 - Michael Baudin

Copyright (C) 2010 - DIGITEO - Michael Baudin

Bibliography

“Compact Numerical Methods for Computers: Linear Algebra and Function Minimisation”, second edition, J.C. Nash, Adam Hilger, Bristol, 1990 (Appendix 1).

“A handbook of numerical matrix inversion and solution of linear equations”, Joan R. Westlake

“Accuracy and Stability of Numerical Algorithms”, A Gallery of Test Matrices , Nicolas Higham

“Mathematical recreations and essays”, 12th ed., W. W. Rouse Ball and H. S. M. Coxeter


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