P-cyclic matrices and the symmetric successive overrelaxation method

Abstract

In this paper, the new functional equation, [λ−(1−ω) 2 ] p =λ[λ+1−ω] p -2 (2−ω) 2 ω p μ p , 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 S ω , 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.