复双共轭梯度法的结构  

Structure of the Complex bi-Conjugate Gradient Method

作　　者：吴海容[1] 

机构地区：[1]哈尔滨电工学院

出　　处：《哈尔滨电工学院学报》1996年第2期133-141,共9页

摘　　要：针对一般复线性方程组的求解问题，文献［１］和［２］用类比于实的双共轭梯度法的方式，提出了复双共轭梯度法。然而到目前为止，还没有文献直接从复方程组出发，推导出此重要算法的计算公式。本文从复方程组出发，先给出两个基本定理，然后通过严格的计算，给出复双共轭梯度法各公式的来源和推导过程，同时讨论了它的收敛性，从而展现出此法的数学结构。The complex bi-conjugate gradient method for solving general linear complex systems proposed by Jacobs is a generalization of real bi-conjugate gradient method by analogy.However,this method hasn't been strictly deduced by mathematical analysis yet. In this paper,a direct approach to the complex systems is adopted. Two basic theorems are proved at first,then the formulae of CBCG algorithm are derived by strict calculation; at last the convergence properties are discussed and the mathematical structure of this method is shown.

关 键 词：共轭梯度法 矩阵论 数学结构 

分 类 号：O151.21[理学—数学]