Optimal preconditioners for functions of matrices
Optimal preconditioners for functions of matrices
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DOI：
10.1016/j.laa.2014.05.023
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发表时间：
2014-09
影响因子：
1.1
通讯作者：
X. Jin;Zhi Zhao;S. Tam
中科院分区：
文献类型：
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作者：
X. Jin;Zhi Zhao;S. Tam
给定矩阵A的最优预条件子cU（A）是T. Chan [6].从那时起，它已被证明是有效的解决一大类结构化系统。本文对矩阵的不同函数构造了最优预条件子。更精确地说，设f是从Cn × n到Cn × n的矩阵的函数。给定A∈ Cn × n，f（A）有两种可能的最优预条件子：cU（f（A））和f（cU（A））.本文研究了不同矩阵函数的cU（f（A））和f（cU（A））的性质。数值实验表明了最优预条件子在求解f（A）x= B时的有效性.
The optimal preconditioner c U (A) of a given matrix A was proposed in 1988 by T. Chan [6]. Since then, it has been proved to be efficient for solving a large class of structured systems. In this paper, we construct the optimal preconditioners for different functions of matrices. More precisely, let f be a function of matrices from C n× n to C n× n. Given A∈ C n× n, there are two possible optimal preconditioners for f (A): c U (f (A)) and f (c U (A)). In the paper, we study properties of both c U (f (A)) and f (c U (A)) for different functions of matrices. Numerical experiments are given to illustrate the efficiency of the optimal preconditioners when they are used to solve f (A) x= b.