On the exact p-cyclic SSOR convergence domains Original Research Article

Suppose that A set membership, variant Cn, n is a block p-cyclic consistently ordered matrix, and let B and Sω denote, respectively, the block Jacobi and the block symmetric successive overrelaxation (SSOR) iteration matrices associated with A. Neumaier and Varga found [in the (varrho(B), ω) plane] the exact convergence and divergence domains of the SSOR method for the class of H-matrices. Hadjidimos and Neumann applied Rouchéʹs theorem to the functional equation connecting the eigenvalue spectra σ(B) and σ(Sω) obtained by Varga, Niethammer, and Cai, and derived in the (varrho(B), ω) plane the convergence domains for the SSOR method associated with p-cyclic consistently ordered matrices, for any p greater-or-equal, slanted 3. In the present work it is further assumed that the eigenvalues of Bp are real of the same sign. Under this assumption the exact convergence domains in the (varrho(B), ω) plane are derived in both the nonnegative and the nonpositive cases for any p greater-or-equal, slanted 3.