Abstract
Linear systems whose associated block Jacobi iteration matrixB is weakly cyclic generated by the cyclic permutation σ = (σ1,σ2,..., σp) in the spirit of Li and Varga are considered. Regions of convergence for the corresponding blockp-cyclic SOR method are derived and the exact convergence domains for real spectra, σ(Bp), of the same sign are obtained. Moreover, analytical expressions for two special cases forp = 5 are given and numerical results are presented confirming the theory developed. The tools used for this work are mainly from complex analysis and extensive use of (asteroidal) hypocycloids in the complex plane is made to produce our results.
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