Nonstationary two-stage multisplitting methods with overlapping blocks

Parallel synchronous two-stage multisplitting methods with overlap for the solution of linear systems of equations are studied. It is shown that under certain hypotheses, the method with overlap is faster, in some measure, than that without overlap, Our results extend the comparison results of multisplittings with overlapping blocks with those of nonoverlapping blocks from (A. Frommer, B. Pohl, A comparison result for multisplittings and wave form relaxation methods, Numer. Linear Algebra Appl, 2 (1995) 335-346) and (M.T. Jones, D.B. Szyld, Two-stage multisplitting methods with overlapping blocks, Numer. Linear Algebra Appl. 3 (1996) 113-124) to the two-stage nonstationary case. (C) 1998 Elsevier Science Inc. All rights reserved.