An Inverse Free Preconditioned Krylov Subspace Method for Symmetric Generalized Eigenvalue Problems
An Inverse Free Preconditioned Krylov Subspace Method for Symmetric Generalized Eigenvalue Problems
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DOI：
10.1137/s1064827500382579
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发表时间：
2002
期刊：
影响因子：
--
通讯作者：
G. Golub;Q. Ye
中科院分区：
文献类型：
--
作者：
G. Golub;Q. Ye
本文提出了一种求对称定广义特征值问题Ax = \lambda B x$的一些极值特征值的无逆Krylov子空间方法。基本方法采用内-外迭代的形式，不涉及B的求逆或任何移位-求逆矩阵$A-\enda_0 B$。收敛性分析，导致一个预处理方案，通过一些等价的特征值问题的转换加速收敛。数值例子说明了收敛性，并证明了该方法的竞争力。
In this paper, we present an inverse free Krylov subspace method for finding some extreme eigenvalues of the symmetric definite generalized eigenvalue problem $Ax = \lambda B x$. The basic method takes a form of inner-outer iterations and involves no inversion of B or any shift-and-invert matrix $A-\lambda_0 B$. A convergence analysis is presented that leads to a preconditioning scheme for accelerating convergence through some equivalent transformations of the eigenvalue problem. Numerical examples are given to illustrate the convergence properties and to demonstrate the competitiveness of the method.