Mathematical Sciences: Faculty Publications

An Adaptive Method for Solving Nonsymmetric Linear Systems Involving Applications of SCPACK

Document Type

Article

Publication Date

12-24-1992

Publication Title

Journal of Computational and Applied Mathematics

DOI

10.1016/0377-0427(92)90006-J

ISSN

0377-0427

Abstract

Consider the following (large) system of linear equations: X = TX + c, where it is assumed that T is an n × n real matrix with 1 excluded from the spectrum of T, and that c is a real vector of dimension n. This paper uses results from function theory, approximation theory and conformal mapping theory, and constructs an adaptive numerical method to solve the system above with the aid of SCPACK. This adaptive method periodically estimates the eigenvalue set to obtain near-asymptotically optimal rates of convergence of the associated (k, l)-step semi-iterative methods.

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