A parallel algorithm for sparse symbolic Cholesky factorization on a multiprocessor
type: Item
instance of: scholarly article
title: A parallel algorithm for sparse symbolic Cholesky factorization on a multiprocessor
zbMATH Open document ID: 0654.65025
DOI: 10.1016/0167-8191(88)90039-7
author: Earl Zmijewski
author: J. R. Gilbert
published in: Parallel Computing
publication date: 1988-01-01T00:00:00Z
review text: Consider a system of linear algebraic equations \(Ax=b\), where A is an \(n\times n\) large sparse symmetric positive definite matrix. Solving it for x the Cholesky factor L of A is computed first and then the systems \(Ly=b\) and \(L^ Tx=y\) are solved, where L is the lower triangular matrix such that \(A=LL^ T\). A parallel algorithm is developed for computing elimination forests and its correctness is proved. Using this algorithm a new parallel symbolic Cholesky factorization algorithm is presented for a message-passing hypercube multiprocessor and its complexity is discussed.
Mathematics Subject Classification ID: 65F05
Mathematics Subject Classification ID: 65Y05
Mathematics Subject Classification ID: 15A23
zbMATH DE Number: 4068161
zbMATH Keywords: large sparse symmetric positive definite matrix
zbMATH Keywords: parallel algorithm
zbMATH Keywords: elimination forests
zbMATH Keywords: parallel symbolic Cholesky factorization algorithm
zbMATH Keywords: message-passing hypercube multiprocessor
zbMATH Keywords: complexity
reviewed by: Lubomír Bakule
MaRDI profile type: Publication
full work available at URL: 0167-8191(88)90039-7
OpenAlex ID: W2023521505
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description: scientific article; zbMATH DE number 4068161