A harmonic Lanczos bidiagonalization method for computing interior singular triplets of large matrices

We propose a harmonic Lanczos bidiagonalization method for computing some interior singular triplets of large matrices. We prove that the approximate singular triplet is convergent if the norm of a certain Rayleigh quotient matrix is uniformly bounded and the approximate singular values are well sep...

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Bibliographic Details
Published in:Applied mathematics and computation 2012-03, Vol.218 (14), p.7459-7467
Main Authors: Niu, Datian, Yuan, Xuegang
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Computation
Harmonic Lanczos bidiagonalization method
Harmonic shifts
Harmonics
Implicit restarting technique
Lanczos bidiagonalization process
Mathematical analysis
Matrices
Matrix methods
Singular triplets
Strategy
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Summary:We propose a harmonic Lanczos bidiagonalization method for computing some interior singular triplets of large matrices. We prove that the approximate singular triplet is convergent if the norm of a certain Rayleigh quotient matrix is uniformly bounded and the approximate singular values are well separated. Combining with the implicit restarting technique, we develop an implicitly restarted harmonic Lanczos bidiagonalization algorithm and suggest a strategy to select shifts. Numerical experiments show that one can use this algorithm to compute the interior singular triplets efficiently.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2012.01.013