Testing for effects of asymmetry and instability on preconditioned iterations of conjugate gradient type. (English) Zbl 0792.65018
A parametrized family of matrices is used to test the performance of some preconditioned iterative methods. The test matrices are based on a simple discretization of a dynamic, two-species, constant coefficients, reaction-diffusion system of partial differential equations. The results appear to confirm observations of other studies that the performance of the methods is essentially uneffected by asymmetry, but is strongly affected by instability.
Reviewer: F.Szidarovszky (Tucson)
MSC:
65F10 | Iterative numerical methods for linear systems |
65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
35K57 | Reaction-diffusion equations |