On The Exact P-Cyclic SSOR Convergence Domains
نویسندگان
چکیده
Suppose that A E (]J',n is a block p-cyclic consistently ordered matrix and let Band Sw denote , respectively, the black Jacobi and the block Symmetric Successive Overrelaxation (SSOR) iteration matrices associated with A. Neumaier a.nd Varga found (in the (p(IBI),w)-plane) the exact convergence and divergence domains of the SSOR method for the class of H-matrice8. Hadjidimos and Neumann applied Rouche's theorem to the functional equation connecting the eigenvalue spectra 17(8) and O'"(S...), obtained by Varga, Niethammer and Cai, and derived in the (p(B),w)-plane the convergence domains for the SSOR method associated with p-cyclic consistently ordered matrices, for any p ~ 3. In the present work it is Curther assumed that the eigenvalues oC BP are real of the same sign. Under this assumption the exact convergence domains in the (p(B),w)-plane are derived in both the nonnegative and the nonpositive cases Cor any p ~ 3.
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On Domains of Superior Convergence of the SSOR Method Over the SOR Method for p- Cyclic H-Matrices
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