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A block Cholesky-LU-based QR factorization for rectangular matrices
Citation Link: https://doi.org/10.15480/882.5036
Publikationstyp
Journal Article
Date Issued
2023-10
Sprache
English
Author(s)
Institut
TORE-DOI
Volume
30
Issue
5
Article Number
e2497
Citation
Numerical Linear Algebra with Applications 30 (5): e2497 (2023-10)
Publisher DOI
Scopus ID
Publisher
Wiley
The Householder method provides a stable algorithm to compute the full QR factorization of a general matrix. The standard version of the algorithm uses a sequence of orthogonal reflections to transform the matrix into upper triangular form column by column. In order to exploit (level 3 BLAS or structured matrix) computational advantages for block-partitioned algorithms, we develop a block algorithm for the QR factorization. It is based on a well-known block version of the Householder method which recursively divides a matrix columnwise into two smaller matrices. However, instead of continuing the recursion down to single matrix columns, we introduce a novel way to compute the QR factors in implicit Householder representation for a larger block of several matrix columns, that is, we start the recursion at a block level instead of a single column. Numerical experiments illustrate to what extent the novel approach trades some of the stability of Householder's method for the computational efficiency of block methods.
Subjects
block QR factorization
Householder method
DDC Class
510: Mathematik
Publication version
publishedVersion
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Numerical Linear Algebra App - 2023 - Le Borne - A block Cholesky‐LU‐based QR factorization for rectangular matrices.pdf
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