Solution of linear least squares via the ABS algorithm
type: Item
instance of: scholarly article
title: Solution of linear least squares via the ABS algorithm
zbMATH Open document ID: 0771.65020
DOI: 10.1007/BF01581261
author: E. Spedicato
author: Elena Bodon
published in: Mathematical Programming. Series A. Series B
publication date: 1993-06-29T00:00:00Z
review text: The authors consider the application of ABS methods to the solution of overdetermined linear systems \(Ax=b\) arising in least squares problems. The general class of ABS algorithms is described in the paper by \textit{J. Abaffy}, \textit{C. G. Broyden} and the first author [Numer. Math. 45, 361- 387 (1985; Zbl 0535.65009)]. This paper gives the specific form required for the least squares implementation, again using rank-one updates for the reflection matrix \(H\). Six implementations are briefly described and the second part describes the results of extensive numerical experiments with these implementations. The authors conclude that an explicit Gram-Schmidt factorization incorporated into a modified Huang algorithm generally gives better results than the NAG QR code, though the latter has smaller overheads.
Mathematics Subject Classification ID: 65F20
Mathematics Subject Classification ID: 65K05
zbMATH DE Number: 221260
zbMATH Keywords: ABS methods
zbMATH Keywords: overdetermined linear systems
zbMATH Keywords: least squares problems
zbMATH Keywords: rank- one updates
zbMATH Keywords: numerical experiments
zbMATH Keywords: Gram-Schmidt factorization
zbMATH Keywords: Huang algorithm
reviewed by: Adrian Swift
describes a project that uses: ESSL
MaRDI profile type: Publication
cites work: A class of direct methods for linear systems
cites work: The local convergence of ABS methods for nonlinear algebraic equations
cites work: Numerical experiments with the symmetric algorithm in the ABS class for linear systems
cites work: Q3995754
cites work: A class of scaled direct methods for linear systems
cites work: Solving linear least squares problems by Gram-Schmidt orthogonalization
cites work: Iterative refinement of linear least squares solutions II
cites work: On the numerical stability of Huang's update
cites work: Reorthogonalization and Stable Algorithms for Updating the Gram-Schmidt QR Factorization
cites work: Singular value decomposition and least squares solutions
cites work: Q4879581
cites work: A direct method for the general solution of a system of linear equations
cites work: Solving linear least squares by orthogonal factorization and pseudoinverse computation via the modified Huang algorithm in the ABS class
cites work: Conjugate direction methods for solving systems of linear equations
cites work: Q3873397
full work available at URL: https://doi.org/10.1007/bf01581261
OpenAlex ID: W2054473470
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description: scientific article; zbMATH DE number 221260