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Nonstationary Multisplittings with General Weighting Matrices

In the convergence theory of multisplittings for symmetric positive definite (s.p.d.) matrices it is usually assumed that the weighting matrices are scalar matrices, i.e., multiples of the identity. In this paper, this restrictive condition is eliminated. In its place it is assumed that more than one (inner) iteration is performed in each processor (or block). The theory developed here is applied to nonstationary multisplittings for s.p. d. matrices, as well as to two-stage multisplittings for symmetric positive semidefinite matrices.