author: Andrisani, E.; Di Lena, G.
shorttitle: An improved dqds type algorithm.
source: Computing 64, No. 1 - 19 (2000)
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 ) 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.