An implicitly restarted block Lanczos bidiagonalization method using Leja shifts

Abstract

In this paper, we propose an implicitly restarted block Lanczos bidiagonalization (IRBLB) method for computing a few extreme or interior singular values and associated right and left singular vectors of a large matrix A. Our method combines the advantages of a block routine, implicit shifting, and the application of Leja points as shifts in the accelerating polynomial. The method neither requires factorization of A nor of a matrix that contains A. This makes the method well suited for very large matrices. For many matrices, the method presented in this paper requires less computational work and computer storage than other available approaches. Computed examples illustrate the performance of the method described.