MINIMIZATION OF THE SPECTRAL NORM OF THE SOR OPERATOR IN A MIXED CASE

Abstract

In this work we solve the problem of the minimization of the spectral norm of the SOR operator associated with a block two-cyclic consistently ordered matrix A epsilon C-n,C-n, assuming that the corresponding Jacobi matrix has eigenvalues mu epsilon [-beta, beta]boolean OR[-iota alpha, iota alpha], with beta epsilon [0, 1), alpha epsilon [0,+infinity) and iota = root-1. Previous results obtained by other researchers are extended.