A PROCESS FOR THE SELECTION OF OVER-RELAXATION FACTOR ω AND THE RELATED COMPUTATION FOR Ax-b

Abstract

A procedure is presented for chooing over-relaxation factor w when we do not posses any knowledge of it. This relaxtion factor however does ,not represent the conventinal sealar mairix in the matrix notarion. Insted, it represents a dagonal matrix having the form diag(w 1..1)A linear system Ax = b is considered for illustration. A few examples worked out by one-srep cyclic process (Gmss-Seiihl rn~thod) and obo by over-relaxajion method (with the over-relaxation facyor obtained in the aforesaid manner) irdicate a much more rapid convrrgurice characteristic of the latter process.