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Dept. of Mathematics and Computer Science (Berlin)

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reviewer: Miloslav Znojil

reviewernum: 9689

revieweremail: znojil@ujf.cas.cz

zblno: DE014455352

author: Andrisani, E.; Di Lena, G.

shorttitle: An improved dqds type algorithm.

source: Computing 64, No. 1 - 19 (2000)

rpclass: 65F15

rsclass: 65K05

keywords:singular values, Cholesky LR methods, SVD

revtext: The standard set of the Fortran 77 routines called ``Lapack" provides algorithms (``dlasq1" bis ``dlasq4") for computation of singular values of a matrix. Their key ingredients are Cholesky factorization and reduction to bidiagonal matrices. Recently, Fernando, Parlett and Beresford (cf. ref [6]) offered their sophistication and called it the ``differential qd" algorithm. In the paper, another step in the direction is made. Main attention is paid to an improvement of the upper bound of the relative variation of the singular values of two bidiagonal matrices. The result is recommended as a guide to the improved auxiliary ``splitting" (i.e., a replacement of an extradiagonal element by zero) in computations. Numerical tests illustrate its merits.

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