A Shift-Deflation Technique for Computing a Large Quantity of Eigenpairs of the Generalized Eigenvalue Problems
A Shift-Deflation Technique for Computing a Large Quantity of Eigenpairs of the Generalized Eigenvalue Problems
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DOI：
10.3390/sym14122547
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发表时间：
2022-12
期刊：
影响因子：
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通讯作者：
Wei Wei-Wei;Xiaoping Chen;Xueying Shi;An Luo
中科院分区：
文献类型：
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作者：
Wei Wei-Wei;Xiaoping Chen;Xueying Shi;An Luo
在本文中，我们提出了一个平移收缩技术的广义特征值问题。该技术由以下两个阶段组成：收敛的特征值的零移位，和这些移位的特征值的紧缩。通过上述技术，我们构造了一个新的广义特征值问题，具有较低的维数，它具有相同的特征值与原来的广义特征值问题，除了收敛的。此外，我们考虑的关系的特征向量之前和之后执行的技术。最后，数值实验验证了该方法的有效性和鲁棒性.
In this paper, we propose a shift-deflation technique for the generalized eigenvalue problems. This technique consists of the following two stages: the shift of converged eigenvalues to zeros, and the deflation of these shifted eigenvalues. By performing the above technique, we construct a new generalized eigenvalue problem with a lower dimension which shares the same eigenvalues with the original generalized eigenvalue problem except for the converged ones. In addition, we consider the relations of the eigenvectors before and after performing the technique. Finally, numerical experiments show the effectiveness and robustness of the proposed method.