Summary: Numer. Math. 39, 113-117 (1982)
On tbe Convergenee of tbe Symmetrie SOR Metbod
for Matriees witb Red-Blaek Ordering
Institut flir Angewandte Mathematik, Universität Karlsruhe (TH), Kaiserstr. 12, 7500 Karlsruhe,
Summary. We prove that if the matrix A has the strueture whieh results
from the so-ealled "red-blaek" ordering and if A is an H-matrix then the
symmetrie SO R method (ealled the SSO R method) is eonvergent for
0< w < 2. In the special ease that A is even an M-matrix we show that the
symmetrie single-step method eannot be aeeelerated by the SSO R method.
Symmetry of the matrix A is not assumed.
Subject Classifications: AMS(MOS): 65FlO CR: 5.14
Let there be given the linear system
where A is a nonsingular n by n matrix. If the diagonal part D of the matrix A