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

Authors:
Nicholas J. Higham
Affiliations:
Department of Mathematics, University of Manchester, Manchester, Ml3 9PL, England
Venue:
ACM Transactions on Mathematical Software (TOMS)
Year:
1988

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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.