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

作者：Niu, Datian^*; Yuan, Xuegang

来源：Applied Mathematics and Computation, 2012, 218(14): 7459-7467.

DOI：10.1016/j.amc.2012.01.013

• Singular triplets
• Lanczos bidiagonalization process
• Harmonic Lanczos bidiagonalization method
• Implicit restarting technique
• Harmonic shifts

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.

• 出版日期2012-3-15
• 单位大连民族大学