Nonstationary multisplittings with general weighting matrices

In the convergence theory of multisplittings for symmetric positive definit e (s.p.d.) matrices it is usually assumed that the weighting matrices are s calar matrices, i.e., multiples of the identity. In this paper, this restri ctive condition is eliminated. In its place it is assumed that more than on e (inner) iteration is performed in each processor (or block). The theory d eveloped here is applied to nonstationary multisplittings for s.p.d. matric es, as well as to two-stage multisplittings for symmetric positive semidefi nite matrices.