Error bounds for some overrelaxation methods

Suppose Ax = b is a system of linear equations where the matrix A is symmet ric positive definite and consistently ordered. Some bounds for \\epsilon(k )\\(2) ill terms of the norms of delta(k) =x(k) -x(k-1) and delta(k+1) = x( k+1)-x(k) and their inner product for the SOR, SSOR, USSOR, MSOR and AOR me thods have been given by many authors. Recently, Li presents a uniform boun d for the overrelaxation methods. In this paper, an error bound for the USM AOR method is derived. As special cases of the USMAOR method, bounds of \\e psilon(k)\\(2) for the SMAOR, USMSOR, SMSOR, USAOR, SAOR, USSOR, SSOR, MAOR , MSOR, AOR, EAOR, EGS I, EGS II, SOR, JOR, Gauss-Seidel and Jacobi methods are obtained.