Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

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J. Korean Math. Soc. 2011; 48(5): 939-952

Printed September 1, 2011

https://doi.org/10.4134/JKMS.2011.48.5.939

Copyright © The Korean Mathematical Society.

Improving the solvability of ill-conditioned systems of linear equations by reducing the condition number of their matrices

Muhammad Farooq and Abdellah Salhi

The University of Essex, The University of Essex

Abstract

This paper is concerned with the solution of ill-conditioned Systems of Linear Equations (SLE's) via the solution of equivalent SLE's which are well-conditioned. A matrix is first constructed from that of the given ill-conditioned system. Then, an adequate right-hand side is computed to make up the instance of an equivalent system. Formulae and algorithms for computing an instance of this equivalent SLE and solving it will be given and illustrated.

Keywords: condition number, systems of linear equations, ill-conditioning, equivalent systems, Schur complement

MSC numbers: 65N12