A general asynchronous block iterative model with related convergence conditions

AbstractThis paper formulates a general time-varying asynchronous block-iterative model. A convergence condition for asynchronous block-iterations based on this model is given, compared to existing conditions for similar and shown to be strictly weaker

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.This research was supported by Spanish DGESIC grant PB98-0977 and by National Science Foundation grants INT-9521226 and DMS-9973219