Necessary and sufficient conditions for the simplification of generalized conjugate-gradient algorithms
type: Item
instance of: scholarly article
title: Necessary and sufficient conditions for the simplification of generalized conjugate-gradient algorithms
zbMATH Open document ID: 0632.65030
DOI: 10.1016/0024-3795(87)90120-0
author: Wayne D. Joubert
author: David M. Young
published in: Linear Algebra and its Applications
publication date: 1987-01-01T00:00:00Z
review text: The efficiency of the usual conjugate gradient method strongly depends on the possibility of obtaining the new direction of search by just taking a proper linear combination of the direction in the former step and the new gradient. In general, the recursion would require to take into consideration up to n of the foregoing directions. The authors consider generalized conjugate gradient algorithms (ORTHOMIN, ORTHORES) to solve non-Hermitian linear systems and give necessary and sufficient conditions on the matrix which allow similar simplified recursions. The paper continues research of \textit{V. Faber} and \textit{T. Manteuffel} [SIAM J. Numer. Anal. 21, 352-362 (1984; Zbl 0546.65010) and ibid. 24, 170-187 (1987; Zbl 0613.65030)] on the method ORTHODIR.
Mathematics Subject Classification ID: 65F10
zbMATH DE Number: 4028736
zbMATH Keywords: conjugate gradient method
zbMATH Keywords: ORTHOMIN
zbMATH Keywords: ORTHORES
zbMATH Keywords: non-Hermitian linear systems
zbMATH Keywords: ORTHODIR
MaRDI profile type: Publication
full work available at URL: 0024-3795(87)90120-0
OpenAlex ID: W1989057852
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description: scientific article; zbMATH DE number 4028736