Picture of virus under microscope

Research under the microscope...

The Strathprints institutional repository is a digital archive of University of Strathclyde research outputs.

Strathprints serves world leading Open Access research by the University of Strathclyde, including research by the Strathclyde Institute of Pharmacy and Biomedical Sciences (SIPBS), where research centres such as the Industrial Biotechnology Innovation Centre (IBioIC), the Cancer Research UK Formulation Unit, SeaBioTech and the Centre for Biophotonics are based.

Explore SIPBS research

Backward error and condition of structured linear systems

Higham, Desmond J. and Higham, Nicholas J. (1992) Backward error and condition of structured linear systems. SIAM Journal on Matrix Analysis and Applications, 13 (1). pp. 162-175. ISSN 0895-4798

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

Abstract

Existing definitions of backward error and condition number for linear systems do not cater to structure in the coefficient matrix, except possibly for sparsity. The definitions are extended so that when the coefficient matrix has structure the perturbed matrix has this structure too. It is shown that when the structure comprises linear dependence on a set of parameters, the structured componentwise backward error is given by the solution of minimal $infty $ -norm to an underdetermined linear system; an explicit expression for the condition number in this linear case is also obtained. Applications to symmetric matrices, Toeplitz matrices and the least squares problem are discussed and illustrated through numerical examples.