k-Part splittings and operator parameter overrelaxation

AbstractThis paper proceeds in two directions of attack for finding (iteratively) solutions for linear systems on Hilbert space. First, we consider scalar-dependent Overrelaxation as a special case of operator-dependent overrelaxations. Secondly, we study “finer” splittings than the conventional two-part splittings and show where, in some cases, these new splittings can either accelerate convergence of approximating sequences derived from two-part splittings or else turn divergent sequences into convergent ones