Exploiting the Composite Step Strategy to the BiconjugateA-Orthogonal Residual Method for Non-Hermitian Linear Systems

Jing, Y.-F., Huang, T.-Z., Carpentieri, B. ORCID: 0000-0002-0516-0033 and Duan, Y., 2013. Exploiting the Composite Step Strategy to the BiconjugateA-Orthogonal Residual Method for Non-Hermitian Linear Systems. Journal of Applied Mathematics, 2013, p. 408167. ISSN 1110-757X

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Abstract

The Biconjugate A-Orthogonal Residual (BiCOR) method carried out in finite precision arithmetic by means of the biconjugate A-orthonormalization procedure may possibly tend to suffer from two sources of numerical instability, known as two kinds of breakdowns, similarly to those of the Biconjugate Gradient (BCG) method. This paper naturally exploits the composite step strategy employed in the development of the composite step BCG (CSBCG) method into the BiCOR method to cure one of the breakdowns called as pivot breakdown. Analogously to the CSBCG method, the resulting interesting variant, with only a minor modification to the usual implementation of the BiCOR method, is able to avoid near pivot breakdowns and compute all the well-defined BiCOR iterates stably on the assumption that the underlying biconjugate A-orthonormalization procedure does not break down. Another benefit acquired is that it seems to be a viable algorithm providing some further practically desired smoothing of the convergence history of the norm of the residuals, which is justified by numerical experiments. In addition, the exhibited method inherits the promising advantages of the empirically observed stability and fast convergence rate of the BiCOR method over the BCG method so that it outperforms the CSBCG method to some extent.

Item Type: Journal article
Publication Title: Journal of Applied Mathematics
Creators: Jing, Y.-F., Huang, T.-Z., Carpentieri, B. and Duan, Y.
Publisher: Hindawi Publishing Corporation
Date: 2013
Volume: 2013
ISSN: 1110-757X
Identifiers:
NumberType
10.1155/2013/408167DOI
Divisions: Schools > School of Science and Technology
Depositing User: Jonathan Gallacher
Date Added: 16 May 2016 12:33
Last Modified: 09 Jun 2017 14:02
URI: http://irep.ntu.ac.uk/id/eprint/27798

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