The use of preconditioning in direct methods of solving positive definite linear systems

Abstract

The concept of preconditioning hitherto successfully applied to accelerate the convergence rate of iterative methods is now extended to the direct methods of solution of small order dense illconditioned matrix systems. It is shown that by solving the equivalent preconditioned linear system using Gaussian elimination and Choleski factorisation methods minimises the rounding errors incurred in the computational process. Theoretical analysis justifying this theory are included together with supporting numerical evidence.

Keywords:

• Preconditioning
• rounding errors
• Gaussian elimination
• Choleski factorisation

C.R. Categories:

• G.1.3