## 2006.179: Componentwise perturbation theory for linear systems with multiple right-hand sides

2006.179:
Desmond J. Higham and Nicholas J. Higham
(1992)
*Componentwise perturbation theory for linear systems with multiple right-hand sides.*
Linear Algebra and its Applications, 174.
pp. 111-129.
ISSN 0024-3795

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DOI: 10.1016/0024-3795(92)90046-D

## 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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Subjects: | MSC 2000 > 15 Linear and multilinear algebra; matrix theory MSC 2000 > 65 Numerical analysis |

MIMS number: | 2006.179 |

Deposited By: | Miss Louise Stait |

Deposited On: | 05 July 2006 |

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