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Superquadratic convergence of DLASQ for computing matrix singular values

โœ Scribed by Kensuke Aishima; Takayasu Matsuo; Kazuo Murota; Masaaki Sugihara

Book ID
104006802
Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
348 KB
Volume
234
Category
Article
ISSN
0377-0427

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โœฆ Synopsis

DLASQ is a routine in LAPACK for computing the singular values of a real upper bidiagonal matrix with high accuracy. The basic algorithm, the so-called dqds algorithm, was first presented by Fernando-Parlett, and implemented as the DLASQ routine by Parlett-Marques. DLASQ is now recognized as one of the most efficient routines for computing singular values. In this paper, we prove the asymptotic superquadratic convergence of DLASQ in exact arithmetic.

๐Ÿ“œ SIMILAR VOLUMES

Some inequalities for singular values of
Some inequalities for singular values of matrix products
โœ Bo-Ying Wang; Bo-Yan Xi ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 213 KB

Let crl(C) >/ ... /> cr,(C) denote the singular values of a matrix C ~ C "xm, and let 1 ~1 k o. r A r k r r ~t=l i,( )orn\\_t+l(B) and ~.kt=lo'tr(AB) ~ Et=lo'~(A)tr,\\_i,+l(B), where A C pร—", B ~ C nxm. We also consider the cases for the product of three matrices and more.