Improving Speed and Accuracy of Krylov Type Linear System Solvers
by
Axel Facius
Institute for Applied Mathematics,

Preconditioned Krylov subspace solvers are an important and frequently used technique for solving large sparse linear systems. There are many advantageous properties concerning convergence rates and error estimates. However, implementing such a solver on a computer, we often observe an unexpected and even contrary behavior. The only reason for this effect is the use of an insufficient arithmetic.

We give some theoretical insight as well as several examples for the direct influence of the machine precision on speed and accuracy of preconditioned Krylov type linear system solvers. The purpose of this talk is to show that this gap between the theoretical and practical behavior can be significantly narrowed by using a suited arithmetic. To verify these more or less heuristic improvements we additionally give rigorous error bounds to our computed results.

Date received: January 10, 2001