Computing eigenpairs in augmented Krylov subspace produced by Jacobi-Davidson correction equation
Computing eigenpairs in augmented Krylov subspace produced by Jacobi-Davidson correction equation
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DOI：
10.1016/j.cam.2018.05.001
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发表时间：
2018-12
期刊：
影响因子：
--
通讯作者：
Cun-Qiang Miao
中科院分区：
文献类型：
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作者：
Cun-Qiang Miao
本文提出了一种增广的Krylov子空间方法，用于计算Hermitian矩阵的一些极值特征值和相应的特征向量。增广Krylov子空间是标准Krylov子空间和另一个用于提取期望特征对近似值的低维子空间的并集，它与Jacobi-Davidson迭代法中涉及的投影子空间有本质的不同。增广Krylov子空间方法具有全局收敛性和局部三次收敛性。数值实验表明了该方法的收敛性和竞争性。
In this paper, we present an augmented Krylov subspace method for computing some extreme eigenvalues and corresponding eigenvectors of Hermitian matrices. The augmented Krylov subspace, which is a union of the standard Krylov subspace and another low-dimension subspace used to extract the approximations to the desired eigenpairs, is essentially different from the projection subspace involved in the Jacobi–Davidson iteration method. The augmented Krylov subspace method converges globally and attains cubic convergence rate locally. Some numerical experiments are carried out to demonstrate the convergence property and the competitiveness of this method.