Picture water droplets

Developing mathematical theories of the physical world: Open Access research on fluid dynamics from Strathclyde

Strathprints makes available Open Access scholarly outputs by Strathclyde's Department of Mathematics & Statistics, where continuum mechanics and industrial mathematics is a specialism. Such research seeks to understand fluid dynamics, among many other related areas such as liquid crystals and droplet evaporation.

The Department of Mathematics & Statistics also demonstrates expertise in population modelling & epidemiology, stochastic analysis, applied analysis and scientific computing. Access world leading mathematical and statistical Open Access research!

Explore all Strathclyde Open Access research...

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

Full text not available in this repository. Request a copy from the Strathclyde author

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.