A Young-Eidsonʹs type algorithm for complex p-cyclic SOR spectra Original Research Article

In a recent work of ours we have solved the problem of the minimization of the spectral radius of the iteration matrix of ap-cyclic successive overrelaxation (SOR) method for the solution of the linear systemAx = b, when the matrixA is blockp-cyclic consistently ordered, for what is known as the “one-point” problem, for anyp greater-or-equal, slanted 3. Particular cases of the “one-point” problem were solved by Young, Varga, Kjellberg, Kredell, Russell and others. In the present work we develop a theory using the results of our previous one and solve first the“two-point” problem special cases of which were solved by Wrigley, Eiermann, Niethammer, Ruttan, Noutsos and others. Secondly, we generalize and extend our theory to cover the“many-point” problem and develop a Young-Eidsonʹs type algorithm for its solution. As possible application areas we mention among others the best blockp-cyclic repartitioning for the SOR method are the solution of large scale systems arising in queueing network problems in Markov analysis.