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

Higham, Nicholas J. (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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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 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theory MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User:	Ms Lucy van Russelt
Date Deposited:	06 Jul 2006
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/366

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