An overview of the Linear Algebra toolbox.
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.
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. | ![]() | ![]() |
Copyright (C) 2008 - 2010 - Michael Baudin
Copyright (C) 2010 - DIGITEO - Michael Baudin
“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