An inexact inverse iteration for large sparse eigenvalue problems
An inexact inverse iteration for large sparse eigenvalue problems
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DOI：
10.1002/(sici)1099-1506(199709/10)4:5
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发表时间：
1997-09
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影响因子：
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通讯作者：
Y. Lai;Kun-Yi Lin;Wen-Wei Lin
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文献类型：
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作者：
Y. Lai;Kun-Yi Lin;Wen-Wei Lin
本文提出了一种计算大型稀疏矩阵最小模特征值及其相关特征向量的逆不精确迭代方法。传统的逆迭代线性系统的求解精度依赖于模量第二小的特征值和迭代次数。证明了该方法保持了逆迭代的线性收敛性。我们还提出了两个实用的精度界公式，在实际应用中得到了应用。©1997 John Wiley & Sons, Ltd
In this paper, we propose an inverse inexact iteration method for the computation of the eigenvalue with the smallest modulus and its associated eigenvector for a large sparse matrix. The linear systems of the traditional inverse iteration are solved with accuracy that depends on the eigenvalue with the second smallest modulus and iteration numbers. We prove that this approach preserves the linear convergence of inverse iteration. We also propose two practical formulas for the accuracy bound which are used in actual implementation. © 1997 John Wiley & Sons, Ltd.