Recently, the accelerated successive overrelaxation- (SOR-) like (ASOR) method was proposed for saddle point problems. In\nthis paper, we establish a generalized accelerated SOR-like (GASOR) method and a modified accelerated SOR-like (MASOR)\nmethod, which are extension of the ASOR method, for solving both nonsingular and singular saddle point problems. The sufficient\nconditions of the convergence (semiconvergence) for solving nonsingular (singular) saddle point problems are derived. Finally,\nnumerical examples are carried out,which show that the GASOR and MASOR vmethods have faster convergence rates than the SORlike,\ngeneralized SOR (GSOR), modified SOR-like (MSOR-like), modified symmetric SOR (MSSOR), generalized symmetric SOR\n(GSSOR), generalized modified symmetric SOR (GMSSOR), and ASOR methods with optimal or experimentally found optimal\nparameters when the iteration parameters are suitably chosen.
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