论文标题
用于计算极端特征值的扩展LOBPCG的收敛分析
Convergence Analysis of Extended LOBPCG for Computing Extreme Eigenvalues
论文作者
论文摘要
本文涉及对局部最佳预处理共轭梯度法（LOBPCG）的延伸变化的收敛分析，该均值对Hermitian矩阵多项式的极端特征值，该矩阵多项式承认了雷利商的某些扩展形式。这项工作是Ovtchinnikov对分析的概括（Siam J.Numer。Anal。，46（5）：2567-2592，2008）。作为实例，确定基质对和双曲双曲线矩阵多项式的算法被证明是全球收敛的，并且具有渐近的局部收敛速率。另外，给出了数值示例以说明收敛性。
This paper is concerned with the convergence analysis of an extended variation of the locally optimal preconditioned conjugate gradient method (LOBPCG) for the extreme eigenvalue of a Hermitian matrix polynomial which admits some extended form of Rayleigh quotient. This work is a generalization of the analysis by Ovtchinnikov (SIAM J. Numer. Anal., 46(5):2567-2592, 2008). As instances, the algorithms for definite matrix pairs and hyperbolic quadratic matrix polynomials are shown to be globally convergent and to have an asymptotically local convergence rate. Also, numerical examples are given to illustrate the convergence.
