ON THE EXACT P-CYCLIC SSOR CONVERGENCE DOMAINS

Suppose that A is an element of C-n,C-n is a block p-cyclic consistent ly ordered matrix, and let B and S-omega denote, respectively, the blo ck Jacobi and the block symmetric successive overrelaxation (SSOR) ite ration matrices associated with A. Neumaier and Varga found [in the (r ho([B]),omega) plane] the exact convergence and divergence domains of the SSOR method for the class of H-matrices. Hadjidimos and Neumann ap plied Rouche's theorem to the functional equation connecting the eigen value spectra sigma(B) and sigma(S-omega) obtained by Varga, Niethamme r, and Cai, and derived in the (rho(B), omega) plane the convergence d omains for the SSOR method associated with p-cyclic consistently order ed matrices, for any rho greater than or equal to 3. In the present wo rk it is further assumed that the eigenvalues of B-rho are real of the same sign. Under this assumption the exact convergence domains in the (rho(B), omega) plane are derived in both the nonnegative and the non positive cases for any rho greater than or equal to 3.