Accurate Singular Values of Bidiagonal Matrices

James Demmel, W. Kahan

Type: Article

Publication Date: 1990-09-01

Citations: 348

DOI: https://doi.org/10.1137/0911052

Abstract

Computing the singular values of a bidiagonal matrix is the final phase of the standard algorithm for the singular value decomposition of a general matrix. A new algorithm that computes all the singular values of a bidiagonal matrix to high relative accuracy independent of their magnitudes is presented. In contrast, the standard algorithm for bidiagonal matrices may compute small singular values with no relative accuracy at all. Numerical experiments show that the new algorithm is comparable in speed to the standard algorithm, and frequently faster.

Locations

SIAM Journal on Scientific and Statistical Computing - View
CiteSeer X (The Pennsylvania State University) - View - PDF

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