Preconditioning for solving Hermite Collocation by the Bi-CGSTAB
نویسندگان
چکیده
Explicit pre/post conditioning of the large, sparse and non-symmetric system of equations, arising from the discretization of the Dirichlet Poisson’s Boundary Value Problem (BVP) by the Hermite Collocation method is the problem considered herein. Using the 2-cyclic (red-black) structure of the Collocation coefficient matrix, we investigate the eigenvalue distribution of its preconditioned analogs emerging from its red-black USSOR (UnSymmetric SOR) splittings. This analysis, coupled with computational efficiency issues, enables us to justify the choice of Gauss-Seidel (GS) preconditioned schemes as efficient and practical ones, when they used to accelerate the rate of convergence of the Bi-CGSTAB iterative Krylov subspace method. Our results are verified by numerical experiments. Key-Words : Collocation, 2-cyclic matrices, Gauss-Seidel, SOR, USSOR, preconditioning, Krylov methods, BiCGSTAB.
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