大型复线性方程组预处理双共轭梯度法

计算机工程与应用 ›› 2007, Vol. 43 ›› Issue (36): 19-20.

大型复线性方程组预处理双共轭梯度法

张永杰,孙秦

西北工业大学航空学院，西安 710072

收稿日期:1900-01-01 修回日期:1900-01-01 出版日期:2007-12-21 发布日期:2007-12-21
通讯作者: 张永杰

Preconditioned bi-conjugate gradient method of large-scale complex linear equations

ZHANG Yong-jie,SUN Qin

School of Aeronautics，Northwestern Polytechnical University，Xi’an 710072，China

Received:1900-01-01 Revised:1900-01-01 Online:2007-12-21 Published:2007-12-21
Contact: ZHANG Yong-jie

摘要/Abstract

摘要： 当复线性方程组的规模较大或系数矩阵的条件数很大时，系数矩阵易呈现病态特性，双共轭梯度法存在不收敛和收敛速度慢的潜在问题，采用适当的预处理技术，可以改善矩阵病态特性，加快收敛速度。从实型不完全Cholesky分解预处理方法出发，构造了一种针对复线性方程组的预处理方法，结合双共轭梯度法，给出了一种预处理双共轭梯度法。数值算例表明该算法求解速度快，可靠高效，能够应用于大型复线性方程组的求解。

关键词: 大型复线性方程组, 不完全Cholesky分解预处理, 双共轭梯度法

Abstract: Coefficient matrix of complex linear equations is generally ill and bi-conjugate gradient method has potential problems on slow convergence or divergence，when complex linear equations are large-scale or condition number of coefficient matrix is too big.Otherwise，appropriate preconditioning techniques can fasten convergence by reducing condition number of ill matrix.Based on the real incomplete Cholesky decomposition precondition，a preconditioned method for complex linear equations is created in this paper，and then a preconditioned bi-conjugate gradient method is obtained by combining the precondition and bi-conjugate gradient method.Numerical examples show that the preconditioned bi-conjugate gradient method is speedy，high-performance and applicable to solve system of large-scale complex linear equations.

Key words: large-scale complex linear equations, incomplete Cholesky decomposition precondition, bi-conjugate gradient method

张永杰,孙秦. 大型复线性方程组预处理双共轭梯度法[J]. 计算机工程与应用, 2007, 43(36): 19-20.

ZHANG Yong-jie,SUN Qin. Preconditioned bi-conjugate gradient method of large-scale complex linear equations[J]. Computer Engineering and Applications, 2007, 43(36): 19-20.