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2006.183: FORTRAN codes for estimating the one-norm of a real or complex matrix, with appliations to condition estimation

2006.183: Nicholas J. Higham (1988) FORTRAN codes for estimating the one-norm of a real or complex matrix, with appliations to condition estimation. ACM Transactions on Mathematical Software, 14 (4). pp. 381-396. ISSN 0098-3500

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DOI: 10.1145/50063.214386

Abstract

FORTRAN 77 codes SONEST and CONEST are presented for estimating the 1-norm ( or the infinity-norm) of a real or complex matrix, respectively. The codes are of wide applicability in condition estimation since explicit access to the matrix, A, is not required; instead, matrix-vector products Ax and ATx are computed by the calling program via a reverse communication interface. The algorithms are based on a convex optimization method for estimating the 1-norm of a real matrix devised by Hager. We derive new results concerning the behavior of Hager's method, extend it to complex matrices, and make several algorithmic modifications in order to improve the reliability and efficiency.

Item Type:Article
Subjects:MSC 2000 > 15 Linear and multilinear algebra; matrix theory
MSC 2000 > 65 Numerical analysis
MIMS number:2006.183
Deposited By:Miss Louise Stait
Deposited On:06 July 2006

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