Exploiting the Composite Step Strategy to the Biconjugate A-Orthogonal Residual Method for Non-Hermitian Linear Systems
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 Gr...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/408167 |
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| Summary: | 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. |
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| ISSN: | 1110-757X 1687-0042 |