Convergence of generalized relaxed multisplitting methods for symmetric positive definite matrices (Q1862017)

The parallel solution of large linear systems with symmetric positive definite (s.p.d.) coefficient matrix by using relaxed multisplitting methods is considered. The diagonally compensated reduction is applied to the multisplitting methods for an s.p.d. matrix. Convergence results for four different variants of relaxed multisplitting methods are given, inter alia a GMJOR (generalized multisplitting Jacobi overrelaxation), a GMSSOR (generalized multisplitting symmetric SOR) and a GMAMOR (generalized multisplitting AMOR). The four methods are compared in terms of their asymptotic convergence rates.