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.
same calculation will su er numerical di culties when there is division by a nonzero number that is relatively small. A= 10 20 1 1 2 When computing the factors Land U, the process does not fail in this case because there is no division by zero. L= 1 0 1020 1 , U= 10 20 1 0 2 10 20
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