A Class of Product-type Methods Based on Lanczos Process
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- ZHANG SHAO-LIANG
- FACULTY OF ENGINEERING, NAGOYA UNIVERSITY
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- FUJINO SEIJI
- FACULTY OF INFORMATION SCIENCES, HIROSHIMA CITY UNIVERSITY
Bibliographic Information
- Other Title
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- ランチョス・プロセスに基づく積型反復解法
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Description
In this paper, we propose a unification of results involving product-type methods for the iterative solution of nonsymmetric linear systems. A characteristic of this class of methods(that includes CGS. Bi-CGSTAB, and Bi-CGSTAB2)is the relationship γ_n=H_n(A)R_n(A)γ_0 where γ_n is the residual vector corresponding to the n-th iterate x_n, and R_n is the Lanczos polynomial generated from Bi-CG. The poly-nomial H_n in the product H_n(A)R_n(A) is chosen to speed up and/or stabilize convergence, while satisfying a standard three-term recurrence relations. Such product-type methods can be regarded as generalizations of Bi-CGSTAB. From the unification, we can see how CGS, Bi-CGSTAB, and Bi-CGSTAB2 fit into a more general framework.
Journal
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- Transactions of the Japan Society for Industrial and Applied Mathematics
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Transactions of the Japan Society for Industrial and Applied Mathematics 5 (4), 343-360, 1995
The Japan Society for Industrial and Applied Mathematics
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Details 詳細情報について
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- CRID
- 1390282680745109504
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- NII Article ID
- 110001883608
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- NII Book ID
- AN10367166
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- ISSN
- 24240982
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- Text Lang
- ja
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- Data Source
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- JaLC
- CiNii Articles
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- Abstract License Flag
- Disallowed