MRTR Method : An Iterative Method Based on the Three-Term Recurrence Formula of CG-Type for Nonsymmetric Matrix
-
- ABE Kuniyoshi
- Graduate School of Human Informatics, Nagoya University
-
- ZHANG Shao-Liang
- Institute of Information Science and Electronics, University of Tsukuba
-
- MITSUI Taketomo
- Graduate School of Human Informatics, Nagoya University
Bibliographic Information
- Other Title
-
- MRTR法:CG型の三項漸化式に基づく非対称行列のための反復解法
- MRTRホウ CGガタ ノ サンコウ ゼンカシキ ニ モトズク ヒタイショウ
Search this article
Abstract
The residual polynomial of GPBi-CG method is represented in the product of the Lanczos polynomial R_k(A), the polynomial H_k(A) similar to the Lanczos but different in parameters, and the starting residual vector. We remove R_k(A) from the residual polynomial, namely, we suggest a new method whose residual vector is the product of the starting one and H_k(A) only. The algorithm, which is called MRTR method, is proven to be mathematically equivalent to the conjugate residual(CR)method. Therefore, we can show its convergence as well as its error bound. However, MRTR method is different from CR method in their implementation. MRTR method has less operation cost than CR method per iteration step. Through numerical experiments of nonsingular and singular linear equations we confirm the equivalence on numerical computations. Moreover, we show that MRTR method is more effective than CR method.
Journal
-
- Transactions of the Japan Society for Industrial and Applied Mathematics
-
Transactions of the Japan Society for Industrial and Applied Mathematics 7 (1), 37-50, 1997
The Japan Society for Industrial and Applied Mathematics
- Tweet
Details 詳細情報について
-
- CRID
- 1390001205768007680
-
- NII Article ID
- 110001883640
-
- NII Book ID
- AN10367166
-
- ISSN
- 09172246
- 24240982
-
- NDL BIB ID
- 4159691
-
- Text Lang
- ja
-
- Data Source
-
- JaLC
- NDL
- CiNii Articles
-
- Abstract License Flag
- Disallowed