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

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

2010-01-19

arxiv.org/abs/1001.3258v1

Mathematics

Numerical Analysis

11 pages, 1 figure, 5 tables

Scientific paper

This paper proposes a harmonic Lanczos bidiagonalization method for computing some interior singular triplets of large matrices. It is shown that the approximate singular triplets are convergent if 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 selection strategy of shifts. Numerical experiments show that one can use this algorithm to compute interior singular triplets efficiently.

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