NDLI: Stability and Sensitivity of Tridiagonal LU Factorization without Pivoting

Content Provider	Springer Nature Link
Author	Bue, M. Isabel Dopico, Froilán M.
Copyright Year	2004
Abstract	In this paper the accuracy of LU factorization of tridiagonal matrices without pivoting is considered. Two types of componentwise condition numbers for the L and U factors of tridiadonal matrices are presented and compared. One type is a condition number with respect to small relative perturbations of each entry of the matrix. The other type is a condition number with respect to small componentwise perturbations of the kind appearing in the backward error analysis of the usual algorithm for the LU factorization. We show that both condition numbers are of similar magnitude. This means that the algorithm is componentwise forward stable, i.e., the forward errors are of similar magnitude to those produced by a componentwise backward stable method. Moreover the presented condition numbers can be computed in O(n) flops, which allows to estimate with low cost the forward errors.
Starting Page	651
Ending Page	673
Page Count	23
File Format	PDF
ISSN	00063835
Journal	BIT Numerical Mathematics
Volume Number	44
Issue Number	4
e-ISSN	15729125
Language	English
Publisher	Kluwer Academic Publishers
Publisher Date	2004-01-01
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	tridiagonal matrices LU factorization condition numbers error analysis Numeric Computing Mathematics Computational Mathematics and Numerical Analysis
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computer Networks and Communications Computational Mathematics Software

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