GSOR

AcronymDefinition
GSORGenealogical Society of Riverside (Riverside, CA)
GSORGeneral Staff Operational Requirements
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and Li and Kong studied the optimal parameters of the GSOR-like and GSOR methods in [5,10], respectively.
In this section, numerical examples illustrate the superiority of the GASOR and MASOR methods to the ASOR, SOR-like, GSOR, and MSOR-like methods when they are used for solving the nonsingular saddle point problem (1) and show the advantages of the GASOR and MASOR methods over the GSOR, GSSOR, MSSOR, and GMSSOR methods for solving the singular saddle point problem (1).
All computations for the SOR-like, GSOR, MSOR-like, ASOR, GASOR, and MASOR methods are started from initial vector [x.sup.(0)] = [([x.sup.(0)T], [y.sup.(0)T]).sup.T] = [(0, 0, ..., 0).sup.T] and the iteration is terminated once the current iterate [x.sup.(k)] satisfies
In Table 2, for various problem sizes p, we list the theoretical optimal iteration parameters of the SOR-like, GSOR, MSOR-like, ASOR, GASOR, and MASOR methods used in our implementations.
We can also see that the spectral radii of the GASOR and MASOR methods in Cases 1 and 2 for this example are almost the same as the ones of the GSOR, MSOR-like and ASOR methods, while the GASOR and MASOR methods require much less time and iteration steps to achieve the stopping criterion than other four methods, and the relaxation parameters of the GASOR and MASOR methods are not optimal and only lie in the convergence region of these methods.
All computations for the GSOR, MSSOR, GSSOR, GMSSOR, GASOR, and MASOR methods are started from initial vector [x.sup.(0)] = [([x.sup.(0)T], [y.sup.(0)T]).sup.T] = [(0, 0, ..., 0).sup.T] and the iteration is terminated once the current iterate [x.sup.(k)] satisfies
In Table 4, for various problem sizes p, we list the theoretical optimal iteration parameters of the iteration matrices of the GSOR, MSSOR, GSSOR, GMSSOR, GASOR, and MASOR methods for solving singular saddle point problem.
The K/Z mapping population will be placed in the Genetic Stocks-Oryza (GSOR) collection at Stuttgart, AR.