Solution of generalized shifted linear systems with complex symmetric matrices
Solution of generalized shifted linear systems with complex symmetric matrices
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DOI：
10.1016/j.jcp.2012.04.046
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发表时间：
2012-07
期刊：
影响因子：
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通讯作者：
T. Sogabe;T. Hoshi;Shaoliang Zhang;T. Fujiwara
中科院分区：
文献类型：
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作者：
T. Sogabe;T. Hoshi;Shaoliang Zhang;T. Fujiwara
我们发展了转移COCG方法[R. Takayama，T. Hoshi，T. Sogabe，S.- L. Zhang，T. Fujiwara，Linear algebraic calculation of绿色函数for large-scale electronic structure theory，Phys. Rev. B 73（165108）（2006）1-9]和移位WQMR方法[T. Sogabe，T. Hoshi，S. L. Zhang，T.李文生，李文生。Anal. 31（2008）126-140]用于求解由电子结构理论产生的具有复对称矩阵的广义移位线性系统。具有适当双线性形式的复对称Lanczos过程在方法的发展中起着重要作用。数值算例表明，当内线性方程组可以有效求解时，该方法具有很强的吸引力。
We develop the shifted COCG method [R. Takayama, T. Hoshi, T. Sogabe, S.-L. Zhang, T. Fujiwara, Linear algebraic calculation of Green’s function for large-scale electronic structure theory, Phys. Rev. B 73 (165108) (2006) 1–9] and the shifted WQMR method [T. Sogabe, T. Hoshi, S.-L. Zhang, T. Fujiwara, On a weighted quasi-residual minimization strategy of the QMR method for solving complex symmetric shifted linear systems, Electron. Trans. Numer. Anal. 31 (2008) 126–140] for solving generalized shifted linear systems with complex symmetric matrices that arise from the electronic structure theory. The complex symmetric Lanczos process with a suitable bilinear form plays an important role in the development of the methods. The numerical examples indicate that the methods are highly attractive when the inner linear systems can efficiently be solved.