Error norm estimation and stopping criteria in preconditioned conjugate gradient iterations

Some techniques suitable for the control of the solution error in the preco nditioned conjugate gradient method are considered and compared. The estima tion can be performed both in the course of the iterations and after their termination. The importance of such techniques follows from the non-existen ce of some reasonable a priori error estimate for very ill-conditioned line ar systems when sufficient information about the right-hand side vector is lacking. Hence, some a posteriori estimates are required, which make it pos sible to verify the quality of the solution obtained for a prescribed light -hand side. The performance of the considered error control procedures is d emonstrated using real-world large-scale linens systems arising in computat ional mechanics. Copyright (C) 2001 John Wiley & Sons, Ltd.