A class of scaled direct methods for linear systems
type: Item
instance of: scholarly article
title: A class of scaled direct methods for linear systems
zbMATH Open document ID: 0714.65026
DOI: 10.1007/BF00050789
author: József Abaffy
author: E. Spedicato
published in: Annals of the Institute of Statistical Mathematics
publication date: 1990-01-01T00:00:00Z
review text: This paper extends the iterative direct method of the authors and \textit{C. Broyden} [Numer. Math. 45, 361-376 (1984; Zbl 0535.65009)] to include scaling of the system matrix \(A_{m\times n}\). Assuming exact arithmetic, a starting vector is updated in m steps to give the solution x of \(Ax=b\). Each update takes 6 steps which can be chosen such that the method mimics the Gauss-Cholesky factorization, the conjugate gradient method and others.
reviewed by: Frank Uhlig
Mathematics Subject Classification ID: 65F05
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 15A12
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65F20
zbMATH DE Number: 4176334
zbMATH Keywords: iterative direct method
zbMATH Keywords: scaling
zbMATH Keywords: Gauss-Cholesky factorization
zbMATH Keywords: conjugate gradient method
MaRDI profile type: Publication
cites work: Q4176349
cites work: Numerical experiments with the symmetric algorithm in the ABS class for linear systems
cites work: Q3677059
cites work: Q3995754
cites work: A class of direct methods for linear systems
cites work: The local convergence of ABS methods for nonlinear algebraic equations
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full work available at URL: https://doi.org/10.1007/bf00050789
OpenAlex ID: W2061686990
description: scientific article; zbMATH DE number 4176334