Generalized product-type methods based on bi-conjugate gradient (GPBiCG) for solving shifted linear systems
Generalized product-type methods based on bi-conjugate gradient (GPBiCG) for solving shifted linear systems
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DOI：
10.1007/s40314-016-0315-y
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发表时间：
2017-12
影响因子：
2.6
通讯作者：
M. Dehghan;Reza Mohammadi-Arani
中科院分区：
文献类型：
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作者：
M. Dehghan;Reza Mohammadi-Arani
GPBiCG是一类乘积型方法的推广，其中残差多项式可以被BiCG的残差多项式和其他具有标准三项递归关系的多项式分解。实际上这个方法泛化了CGS和BiCGStab方法。本文利用GPBiCG给出了一种求解位移线性系统的新方法。GPBiCG比bicstab更快，收敛速度比CGS更平稳。因此，在这里，我们期望开发一种比移位的BiCGStab和移位的CGS方法更快，收敛更平滑的方法来求解移位的线性系统。
GPBiCG is a generalization of a class of product-type methods where the residual polynomials can be factored by the residual polynomial of BiCG and other polynomials with standard three-term recurrence relations. Actually this method generalizes CGS and BiCGStab methods. In this paper we use GPBiCG to present a new method for solving shifted linear systems. GPBiCG is faster than BiCGStab and its convergence is smoother than CGS. So here we are expecting to develop a method which is faster and its convergence is smoother than shifted BiCGStab and shifted CGS methods for solving shifted linear systems.