Transcription of Pivoting for LU Factorization - UPS
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Pivoting for LU Factorization - UPS
Pivoting forLUFactorizationMatthew W. ReidApril 21, 2014 University of Puget SoundE-mail: (C) 2014 Matthew W. Reid. Permission is granted to copy, distribute and/or modifythis document under the terms of the GNU Free Documentation License, Version or any laterversion published by the Free Software Foundation; with no Invariant Sections, no Front-CoverTexts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNUFree Documentation License .1 INTRODUCTION11 IntroductionPivoting forLUfactorization is the process of systematically selecting pivots for Gaussian elimina-tion during theLUfactorization of a matrix . TheLUfactorization is closely related to Gaussianelimination, which is unstable in its pure form. To guarantee the elimination process goes to com-pletion, we must ensure that there is a nonzero pivot at every step of the elimination process.
tation matrix P, which is the identity matrix with rows 1 and 3 swapped. To interchange columns 1 and 3 of the matrix A, we left multiply by the same permutation matrix P. At each step kof Gaussian elimination we encounter an optional row interchange, represented by P k, before eliminat-ing entries via the lower triangular elementary matrix M k ...
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