Stability analysis of a householder-based algorithm for downdating the Cholesky factorization

In this paper a new algorithm for downdating the Cholesky factorization is presented and analyzed. The algorithm is based on Householder transformations. It is less expensive than algorithms based on Givens rotations if more than one row is to be removed from the Cholesky product. Rounding error ana...

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Bibliographic Details
Published inSIAM journal on scientific and statistical computing Vol. 12; no. 6; pp. 1255 - 1265
Main Authors BOJANCZYK, A. X, STEINHARDT, A. O
Format Journal Article
LanguageEnglish
Published Philadelphia, PA Society for Industrial and Applied Mathematics 01.11.1991
Subjects
Algorithms
Cost control
Error analysis
Exact sciences and technology
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Sciences and techniques of general use
Triangulation
Cholesky method
Factorization
Numerical stability
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Summary:In this paper a new algorithm for downdating the Cholesky factorization is presented and analyzed. The algorithm is based on Householder transformations. It is less expensive than algorithms based on Givens rotations if more than one row is to be removed from the Cholesky product. Rounding error analysis shows that the new method is as stable as the rotation-based methods for solving this problem.
ISSN:0196-5204
1064-8275
2168-3417
1095-7197
DOI:10.1137/0912067