On Multisplitt ing Methods and m-Step Preconditioners for Parallel and Vector Machines
APOSTOLOS HADJIDIMOS, A. Yeyios · Purdue e-Pubs (Purdue University System) · 1992
To solve the real nonsingular linear system Ax = b (1) on parallel and vector machines, we consider multisplitting methods, m-step preconditioners and m-step additive preconditioners, generalizing some of the results and methods developed in previous related works.In particular we generalize the method and the corresponding convergence results in [14], and determine suitable relaxed m-step preconditioners ([1], [6]) treating also the problem of minimizing the related condition number, with respect to the relaxation (extrapolation) parameter involved, in various cases.We also generalize the theory for determining suitable m-step additive preconditioners [2] and finally we solve completely the problem of determining the optimum SOR-additive iterative method [2] for 2-cyclic positive definite matrices.