p-cyclic matrices and the symmetric successive overrelaxation method

AbstractIn this paper, the new functional equation, [λ−(1−ω)2]p=λ[λ+1−ω]p-2(2−ω)2ωpμp, which connects the eigenvalues μ of a particular weakly cyclic (of index p) Jacobi matrix B to the eigenvalues λ of its associated symmetric successive overrelaxation (SSOR) matrix Sω, is derived. This functional equation is then applied to the problem of determining bounds for the intervals of convergence and divergence of the SSOR iterative method for classes of H-matrices