MINIMIZATION OF THE SPECTRAL NORM OF THE SOR OPERATOR IN A MIXED CASE
APOSTOLOS HADJIDIMOS, P. Stratis · 2007
Dedicated to Gene Golub on the occasion of his 75th birthday 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 ∈ C n,n, assuming that the corresponding Jacobi matrix has eigenvalues µ ∈ [−β, β] ∪ [−ıα, ıα], with β ∈ [0,1), α ∈ [0,+∞) and ı = √ −1. Previous results obtained by other researchers are extended. Key words. Jacobi and SOR iteration matrices, block two-cyclic consistently ordered matrix, spectral matrix norm AMS subject classifications. 65F10 1. Introduction. It