POLYNOMIAL PRECONDITIONING IN KRYLOV-ROW-METBODS

Krylov methods, which may be used for solving the stage equations in R OW-methods, become increasingly expensive if large subspace dimensions are necessary. We show, that it is possible to switch adaptively to a polynomially preconditioned Krylov process if this situation occurs. We present an algorithm for condensation of the basis of the original Krylov subspace to the smaller basis of the preconditioned subspace. N umerical experiments confirm savings in time and memory requirements f or small polynomial degree. (C) 1998 Elsevier Science B.V. and IMACS. All rights reserved.