On systolic arrays for updating the Cholesky factorization
type: Item
instance of: scholarly article
title: On systolic arrays for updating the Cholesky factorization
zbMATH Open document ID: 0617.65012
DOI: 10.1007/BF01935052
author: Robert Schreiber
author: Wei-Pai Tang
published in: BIT
publication date: 1986-01-01T00:00:00Z
review text: The authors are concerned with finding the Cholesky factors of a matrix \(B=A+\sum^{k}_{1}\alpha_ iz_ iz^ T_ i\) when the factors of A, the constants \(\alpha_ i\) and the vectors \(z_ i\) are known. They implement algorithms studied by \textit{P. Gill}, \textit{G. Golub}, \textit{W. Murray} and \textit{M. Saunders} [(*) Math. Comput. 28, 505-535 (1974; Zbl 0289.65021)] on systolic arrays involving plane rotations [e.g., the first author, BIT 26, 303-316 (1986; reviewed above)]. When \(\alpha_ i>0\) for \(i=1,...,k\), an algorithm from (*) is implemented in a single-pass array. When some \(\alpha_ i\leq 0\), the authors first generalize an algorithm from (*) and then show it can be implemented in a two-pass array.
Mathematics Subject Classification ID: 65F05
Mathematics Subject Classification ID: 15A23
zbMATH DE Number: 4001299
zbMATH Keywords: systolic implementation
zbMATH Keywords: elimination
zbMATH Keywords: Cholesky factorization
zbMATH Keywords: systolic arrays
zbMATH Keywords: plane rotations
reviewed by: Myron Sussman
MaRDI profile type: Publication
cites work: Methods for Modifying Matrix Factorizations
cites work: Systolic Networks for Orthogonal Decompositions
cites work: Q3319684
full work available at URL: https://doi.org/10.1007/bf01935052
OpenAlex ID: W1978050836
description: scientific article; zbMATH DE number 4001299