Abstract This paper focuses on the inner iteration that arises in inexact inverse subspace iteration for computing a small deflating subspace of a large matrix pencil. First, it is shown that the method achieves linear rate of convergence if the inner iteration is performed with increasing accuracy. Then, as inner iteration, block-GMRES is used with preconditioners generalizing the one by Robbé, Sadkane and Spence [Inexact inverse subspace iteration with preconditioning applied to non-Hermitian eigenvalue problems, SIAM J. Matrix Anal. Appl. 31 2009, 1, 92–113]. It is shown that the preconditioners help to maintain the number of iterations needed by block-GMRES to approximately a small constant. The efficiency of the preconditioners is illustrated by numerical examples.

中文翻译：

---

广义特征值问题不精确逆子空间迭代的收敛和预处理

摘要 本文重点研究了在计算大矩阵铅笔的小收缩子空间的不精确逆子空间迭代中出现的内部迭代。首先，表明如果以增加的精度执行内部迭代，则该方法实现线性收敛速度。然后，作为内部迭代，块 GMRES 与由 Robbé、Sadkane 和 Spence [Inexact inverse subspace iteration with preconditioning应用于非 Hermitian 特征值问题，SIAM J. Matrix Anal. 应用程序 31 2009, 1, 92–113]。结果表明，预处理器有助于将块 GMRES 所需的迭代次数保持在大约一个小的常数。数值例子说明了预处理器的效率。