Dynamic control of a BICGSTAB algorithm

In many scientific fields, KRYLOV-type methods prove to be very powerful. N evertheless, they are prone to rounding errors that slow down their converg ence rate. Some of these methods, like the BICGSTAB method, are also subjec t to breakdowns and near-breakdowns, situations where a denominator is zero or very affected by rounding errors. Generally, the last case is detected by means of the classical inequality /x/ < epsilon in floating-point arithm etic but it is very sensitive to epsilon values. The discrete stochastic ar ithmetic enables us to estimate the accuracy of intermediate results and to avoid us from these a priori choices, Look ahead techniques allow to carry on computations, but sometimes, it is necessary or at least more advantage ous to restart the algorithm, The aim of this paper is to present a dynamic strategy which allows to detect breakdowns and near-breakdowns and to choo se between a look ahead technique and a restart. (C) 2000 IMACS. Published by Elsevier Science B.V. All rights reserved.