A Filtered Lanczos Procedure for Extreme and Interior Eigenvalue Problems
A Filtered Lanczos Procedure for Extreme and Interior Eigenvalue Problems
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DOI：
10.1137/110836535
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发表时间：
2012-08
期刊：
影响因子：
--
通讯作者：
Haw-ren Fang;Y. Saad
中科院分区：
文献类型：
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作者：
Haw-ren Fang;Y. Saad
When combined with Krylov projection methods, polynomial filtering can provide a powerful method for extracting extreme or interior eigenvalues of large sparse matrices. This general approach can be quite efficient in the situation when a large number of eigenvalues is sought. However, its competitiveness depends critically on a good implementation. This paper presents a technique based on such a combination to compute a group of extreme or interior eigenvalues of a real symmetric (or complex Hermitian) matrix. The technique harnesses the effectiveness of the Lanczos algorithm with partial reorthogonalization and the power of polynomial filtering. Numerical experiments indicate that the method can be far superior to competing algorithms when a large number of eigenvalues and eigenvectors is to be computed.
