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

2010/01/19 by Datian Niu, Niu, Datian, Xuegang Yuan +1
Computer Science · Mathematics · Physics and Astronomy · #15A18 #65F15 #Advanced Optimization Algorithms Research #Electromagnetic Scattering and Analysis #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1001.3258

openalex publication_date 2010/01/19 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

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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