# Componentwise perturbation theory for linear systems with multiple right-hand sides

Higham, D.J. and Higham, N.J.
(1992)
*Componentwise perturbation theory for linear systems with multiple right-hand sides.*
Linear Algebra and Its Applications, 174.
pp. 111-130.
ISSN 0024-3795

## Abstract

Existing definitions of componentwise backward error and componentwise condition number for linear systems are extended to systems with multiple right-hand sides and to a general class of componentwise measure of perturbations involving Hölder p-norms. It is shown that for a system of order n with r right-hand sides, the componentwise backward error can be computed by finding the minimum p-norm solutions to n underdetermined linear systems, and an explicit expression is obtained in the case r = 1. A perturbation bound is derived, and from this the componentwise condition number is obtained to within a multiplicative constant. Applications of the results are discussed to invariant subspace computations, quasi-Newton methods based on multiple secant equations, and an inverse ODE problem.

Item type: | Article |
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ID code: | 201 |

Keywords: | componentwise backward error, numerical mathematics, linear systems, Hölder p-norms, Mathematics, Discrete Mathematics and Combinatorics, Algebra and Number Theory, Geometry and Topology, Numerical Analysis |

Subjects: | Science > Mathematics |

Department: | Faculty of Science > Mathematics and Statistics |

Depositing user: | Ms Sarah Scott |

Date Deposited: | 15 Mar 2006 |

Last modified: | 29 Apr 2016 07:16 |

URI: | http://strathprints.strath.ac.uk/id/eprint/201 |