RIGOROUS PERTURBATION BOUNDS OF SOME MATRIX FACTORIZATIONS

This article presents rigorous normwise perturbation bounds for the Cholesky, LU, and QR factorizations with normwise or componentwise perturbations in the given matrix. The considered componentwise perturbations have the form of backward rounding errors for the standard factorization algorithms. Th...

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Bibliographic Details
Published in:SIAM journal on matrix analysis and applications 2010-01, Vol.31 (5), p.2841-2859
Main Authors: CHANG, X.-W, STEHLE, D
Format: Article
Language:English
Subjects:
Algebra
Algorithms
Error analysis
Errors
Exact sciences and technology
Factorization
Finite differences and functional equations
Linear and multilinear algebra, matrix theory
Mathematical analysis
Mathematical problems
Mathematics
Matrix
Numerical Analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Optimization algorithms
Perturbation methods
Rounding
Sciences and techniques of general use
Studies
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Summary:This article presents rigorous normwise perturbation bounds for the Cholesky, LU, and QR factorizations with normwise or componentwise perturbations in the given matrix. The considered componentwise perturbations have the form of backward rounding errors for the standard factorization algorithms. The used approach is a combination of the classic and refined matrix equation approaches. Each of the new rigorous perturbation bounds is a small constant multiple of the corresponding first-order perturbation bound obtained by the refined matrix equation approach in the literature and can be estimated efficiently. These new bounds can be much tighter than the existing rigorous bounds obtained by the classic matrix equation approach, while the conditions for the former to hold are almost as moderate as the conditions for the latter to hold. [PUBLICATION ABSTRACT]
ISSN:0895-4798
1095-7162
DOI:10.1137/090778535