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Volume 1, Issue 2
An Extension of the COCR Method to Solving Shifted Linear Systems with Complex Symmetric Matrices

Tomohiro Sogabe & Shao-Liang Zhang

DOI: 10.4208/eajam.260410.240510a

East Asian J. Appl. Math., 1 (2011), pp. 97-107.

Published online: 2018-02

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  • Abstract

The Conjugate Orthogonal Conjugate Residual (COCR) method [T. Sogabe and S.-L. Zhang, JCAM, 199 (2007), pp. 297-303.] has recently been proposed for solving complex symmetric linear systems. In the present paper, we develop a variant of the COCR method that allows the efficient solution of complex symmetric shifted linear systems. Some numerical examples arising from large-scale electronic structure calculations are presented to illustrate the performance of the variant.

  • Keywords

Shifted linear systems, complex symmetric matrices, COCR, Krylov subspace methods, electronic structure calculation.

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COPYRIGHT: © Global Science Press

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@Article{EAJAM-1-97, author = {Tomohiro Sogabe and Shao-Liang Zhang}, title = {An Extension of the COCR Method to Solving Shifted Linear Systems with Complex Symmetric Matrices}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {1}, number = {2}, pages = {97--107}, abstract = {

The Conjugate Orthogonal Conjugate Residual (COCR) method [T. Sogabe and S.-L. Zhang, JCAM, 199 (2007), pp. 297-303.] has recently been proposed for solving complex symmetric linear systems. In the present paper, we develop a variant of the COCR method that allows the efficient solution of complex symmetric shifted linear systems. Some numerical examples arising from large-scale electronic structure calculations are presented to illustrate the performance of the variant.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.260410.240510a}, url = {http://global-sci.org/intro/article_detail/eajam/10899.html} }
TY - JOUR T1 - An Extension of the COCR Method to Solving Shifted Linear Systems with Complex Symmetric Matrices AU - Tomohiro Sogabe & Shao-Liang Zhang JO - East Asian Journal on Applied Mathematics VL - 2 SP - 97 EP - 107 PY - 2018 DA - 2018/02 SN - 1 DO - http://doi.org/10.4208/eajam.260410.240510a UR - https://global-sci.org/intro/article_detail/eajam/10899.html KW - Shifted linear systems, complex symmetric matrices, COCR, Krylov subspace methods, electronic structure calculation. AB -

The Conjugate Orthogonal Conjugate Residual (COCR) method [T. Sogabe and S.-L. Zhang, JCAM, 199 (2007), pp. 297-303.] has recently been proposed for solving complex symmetric linear systems. In the present paper, we develop a variant of the COCR method that allows the efficient solution of complex symmetric shifted linear systems. Some numerical examples arising from large-scale electronic structure calculations are presented to illustrate the performance of the variant.

Tomohiro Sogabe and Shao-Liang Zhang. (2018). An Extension of the COCR Method to Solving Shifted Linear Systems with Complex Symmetric Matrices. East Asian Journal on Applied Mathematics. 1 (2). 97-107. doi:10.4208/eajam.260410.240510a
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