The computation of bounds for the norm of the error in the conjugate gradient algorithm
type: Item
instance of: scholarly article
title: The computation of bounds for the norm of the error in the conjugate gradient algorithm
zbMATH Open document ID: 0897.65026
DOI: 10.1023/A:1019178811767
published in: Numerical Algorithms
publication date: 1998-10-05T00:00:00Z
review text: The computation of bounds for the norm of the error in the conjugate gradient algorithm is considered. Section 2 recalls how to compute approximations of the A-norm and shows these approximations are lower and upper bounds. Section 3 shows how to compute approximations of the \(l_2\)-norm. Section 4 introduces an adaptive algorithm that computes estimates of the smallest eigenvalue that is needed to obtain upper bounds of the norm. Some numerical experiments showing the effectiveness of this approach are given in the last section.
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65F50
zbMATH DE Number: 1146039
zbMATH Keywords: error bounds
zbMATH Keywords: extreme eigenvalues
zbMATH Keywords: conjugate gradient algorithm
zbMATH Keywords: adaptive algorithm
zbMATH Keywords: numerical experiments
author: G. Meurant
reviewed by: Shenquan Xie
MaRDI profile type: Publication
full work available at URL: a:1019178811767
OpenAlex ID: W26707179
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description: scientific article; zbMATH DE number 1146039