NDLI: Error Estimation in Preconditioned Conjugate Gradients

Content Provider	Springer Nature Link
Author	Strakoš, Zdeněk Tichý, Petr
Copyright Year	2005
Abstract	In practical problems, iterative methods can hardly be used without some acceleration of convergence, commonly called preconditioning, which is typically achieved by incorporation of some (incomplete or modified) direct algorithm as a part of the iteration. Effectiveness of preconditioned iterative methods increases with possibility of stopping the iteration when the desired accuracy is reached. This requires, however, incorporating a proper measure of achieved accuracy as a part of computation.The goal of this paper is to describe a simple and numerically reliable estimation of the size of the error in the preconditioned conjugate gradient method. In this way this paper extends results from [Z. Strakoš and P. Tichý, ETNA, 13 (2002), pp. 56–80] and communicates them to practical users of the preconditioned conjugate gradient method.
Starting Page	789
Ending Page	817
Page Count	29
File Format	PDF
ISSN	00063835
Journal	BIT Numerical Mathematics
Volume Number	45
Issue Number	4
e-ISSN	15729125
Language	English
Publisher	Springer-Verlag
Publisher Date	2005-01-01
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	preconditioned conjugate gradient method error bounds stopping criteria evaluation of convergence numerical stability finite precision arithmetic rounding errors Numeric Computing Mathematics Computational Mathematics and Numerical Analysis
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computer Networks and Communications Computational Mathematics Software

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