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...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
|
| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/408167 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832564148199751680 |
|---|---|
| author | Yan-Fei Jing Ting-Zhu Huang Bruno Carpentieri Yong Duan |
| author_facet | Yan-Fei Jing Ting-Zhu Huang Bruno Carpentieri Yong Duan |
| author_sort | Yan-Fei Jing |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-d001ff38c73348fbb2d88d90092cba93 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-d001ff38c73348fbb2d88d90092cba932025-02-03T01:11:45ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/408167408167Exploiting the Composite Step Strategy to the Biconjugate A-Orthogonal Residual Method for Non-Hermitian Linear SystemsYan-Fei Jing0Ting-Zhu Huang1Bruno Carpentieri2Yong Duan3School of Mathematical Sciences, Institute of Computational Science, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, ChinaSchool of Mathematical Sciences, Institute of Computational Science, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, ChinaInstitute of Mathematics and Computing Science, University of Groningen, Nijenborgh 9, P.O. Box 407, 9700 AK Groningen, The NetherlandsSchool of Mathematical Sciences, Institute of Computational Science, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, ChinaThe 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.http://dx.doi.org/10.1155/2013/408167 |
| spellingShingle | Yan-Fei Jing Ting-Zhu Huang Bruno Carpentieri Yong Duan Exploiting the Composite Step Strategy to the Biconjugate A-Orthogonal Residual Method for Non-Hermitian Linear Systems Journal of Applied Mathematics |
| title | Exploiting the Composite Step Strategy to the Biconjugate A-Orthogonal Residual Method for Non-Hermitian Linear Systems |
| title_full | Exploiting the Composite Step Strategy to the Biconjugate A-Orthogonal Residual Method for Non-Hermitian Linear Systems |
| title_fullStr | Exploiting the Composite Step Strategy to the Biconjugate A-Orthogonal Residual Method for Non-Hermitian Linear Systems |
| title_full_unstemmed | Exploiting the Composite Step Strategy to the Biconjugate A-Orthogonal Residual Method for Non-Hermitian Linear Systems |
| title_short | Exploiting the Composite Step Strategy to the Biconjugate A-Orthogonal Residual Method for Non-Hermitian Linear Systems |
| title_sort | exploiting the composite step strategy to the biconjugate a orthogonal residual method for non hermitian linear systems |
| url | http://dx.doi.org/10.1155/2013/408167 |
| work_keys_str_mv | AT yanfeijing exploitingthecompositestepstrategytothebiconjugateaorthogonalresidualmethodfornonhermitianlinearsystems AT tingzhuhuang exploitingthecompositestepstrategytothebiconjugateaorthogonalresidualmethodfornonhermitianlinearsystems AT brunocarpentieri exploitingthecompositestepstrategytothebiconjugateaorthogonalresidualmethodfornonhermitianlinearsystems AT yongduan exploitingthecompositestepstrategytothebiconjugateaorthogonalresidualmethodfornonhermitianlinearsystems |