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Volume 32, Issue 3
Generalized Conjugate A-Orthogonal Residual Squared Method for Complex Non-Hermitian Linear Systems

Jianhua Zhang & Hua Dai

DOI: 10.4208/jcm.1401-CR13

J. Comp. Math., 32 (2014), pp. 248-265.

Published online: 2014-06

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  • Abstract

Recently numerous numerical experiments on realistic calculation have shown that the conjugate A-orthogonal residual squared (CORS) method is often competitive with other popular methods. However, the CORS method, like the CGS method, shows irregular convergence, especially appears large intermediate residual norm, which may lead to worse approximate solutions and slower convergence rate. In this paper, we present a new product-type method for solving complex non-Hermitian linear systems based on the biconjugate A-orthogonal residual (BiCOR) method, where one of the polynomials is a BiCOR polynomial, and the other is a BiCOR polynomial with the same degree corresponding to different initial residual. Numerical examples are given to illustrate the effectiveness of the proposed method.

  • Keywords

Krylov subspace, BiCOR method, CORS method, Complex non-Hermitian linear systems.

  • AMS Subject Headings

65F10.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-32-248, author = {Jianhua Zhang and Hua Dai}, title = {Generalized Conjugate A-Orthogonal Residual Squared Method for Complex Non-Hermitian Linear Systems}, journal = {Journal of Computational Mathematics}, year = {2014}, volume = {32}, number = {3}, pages = {248--265}, abstract = {

Recently numerous numerical experiments on realistic calculation have shown that the conjugate A-orthogonal residual squared (CORS) method is often competitive with other popular methods. However, the CORS method, like the CGS method, shows irregular convergence, especially appears large intermediate residual norm, which may lead to worse approximate solutions and slower convergence rate. In this paper, we present a new product-type method for solving complex non-Hermitian linear systems based on the biconjugate A-orthogonal residual (BiCOR) method, where one of the polynomials is a BiCOR polynomial, and the other is a BiCOR polynomial with the same degree corresponding to different initial residual. Numerical examples are given to illustrate the effectiveness of the proposed method.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1401-CR13}, url = {http://global-sci.org/intro/article_detail/jcm/9883.html} }
TY - JOUR T1 - Generalized Conjugate A-Orthogonal Residual Squared Method for Complex Non-Hermitian Linear Systems AU - Jianhua Zhang & Hua Dai JO - Journal of Computational Mathematics VL - 3 SP - 248 EP - 265 PY - 2014 DA - 2014/06 SN - 32 DO - http://doi.org/10.4208/jcm.1401-CR13 UR - https://global-sci.org/intro/article_detail/jcm/9883.html KW - Krylov subspace, BiCOR method, CORS method, Complex non-Hermitian linear systems. AB -

Recently numerous numerical experiments on realistic calculation have shown that the conjugate A-orthogonal residual squared (CORS) method is often competitive with other popular methods. However, the CORS method, like the CGS method, shows irregular convergence, especially appears large intermediate residual norm, which may lead to worse approximate solutions and slower convergence rate. In this paper, we present a new product-type method for solving complex non-Hermitian linear systems based on the biconjugate A-orthogonal residual (BiCOR) method, where one of the polynomials is a BiCOR polynomial, and the other is a BiCOR polynomial with the same degree corresponding to different initial residual. Numerical examples are given to illustrate the effectiveness of the proposed method.

Jianhua Zhang and Hua Dai. (2014). Generalized Conjugate A-Orthogonal Residual Squared Method for Complex Non-Hermitian Linear Systems. Journal of Computational Mathematics. 32 (3). 248-265. doi:10.4208/jcm.1401-CR13
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