Stable computation of generalized singular values

Conference · Tue Dec 31 04:00:00 EST 1996

OSTI ID:433400

Drmac, Z; Jessup, E R ^[1]

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1. Univ. of Colorado, Boulder, CO (United States)

We study floating-point computation of the generalized singular value decomposition (GSVD) of a general matrix pair (A, B), where A and B are real matrices with the same numbers of columns. The GSVD is a powerful analytical and computational tool. For instance, the GSVD is an implicit way to solve the generalized symmetric eigenvalue problem Kx = {lambda}Mx, where K = A{sup {tau}}A and M = B{sup {tau}}B. Our goal is to develop stable numerical algorithms for the GSVD that are capable of computing the singular value approximations with the high relative accuracy that the perturbation theory says is possible. We assume that the singular values are well-determined by the data, i.e., that small relative perturbations {delta}A and {delta}B (pointwise rounding errors, for example) cause in each singular value {sigma} of (A, B) only a small relative perturbation {vert_bar}{delta}{sigma}{vert_bar}/{sigma}.

• Research Organization: Front Range Scientific Computations, Inc., Lakewood, CO (United States)
• OSTI ID: 433400
• Report Number(s): CONF-9604167--Vol.1; ON: DE96015306
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ACCURACY
ALGORITHMS
CALCULATION METHODS
EIGENVALUES
ERRORS
ITERATIVE METHODS
MATRICES
PERFORMANCE
PERTURBATION THEORY