The Mathematical Institute, University of Oxford, Eprints Archive

The convergence of iterative solution methods for symmetric and indefinite linear systems

Wathen, A. J. and Fischer, B. and Silvester, David (1997) The convergence of iterative solution methods for symmetric and indefinite linear systems. Technical Report. Unspecified. (Submitted)

[img]
Preview
PDF
167Kb

Abstract

Iterative solution methods provide the only feasible alternative to direct methods for very large scale linear systems such as those which derive from approximation of many partial differential equation problems. For symmetric and positive definite coefficient matrices the conjugate gradient method provides an efficient and popular solver, especially when employed with an appropriate preconditioner. Part of the success of this method is attributable to the rigorous and largely descriptive convergence theory which enables very large sized problems to be tackled with confidence.

Here we describe some convergence results for symmetric and indefinite coefficient matrices which depend on an asymptotically small parameter such as the mesh size in a finite difference or finite element discretisation. These estimates are seen to be descriptive in numerical calculations.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1311
Deposited By:Lotti Ekert
Deposited On:09 Jun 2011 08:23
Last Modified:09 Jun 2011 08:23

Repository Staff Only: item control page