A comparison result for multisplittings and waveform relaxation methods

Abstract

Abstract We show that certain multisplitting iterative methods based on overlapping blocks yield faster convergence than corresponding nonoverlapping block iterations, provided the coefficient matrix is an M‐matrix. This result can be used to compare variants of the waveform relaxation algorithm for solving initial value problems. The methods under consideration use the same discretization technique, but are based on multisplittings with different overlaps. Numerical experiments on the Intel iPSC/860 hypercube are included.