Analytic formulae are obtained for the smoothing factors yielded by Gauss-Seidel relaxation in two-color ordering for a class of scalar elliptic operators. Block and point relaxation, in conjunction with full or partial coarsening, are encompassed for operators with general (constant, positive) coeecients in general dimensions and for an arbitrary number of relaxation sweeps. It is found that t...

We study the semiconvergence of Gauss-Seidel iterative methods for the least squares solution of minimal norm of rank deficient linear systems of equations. Necessary and sufficient conditions for the semiconvergence of the Gauss-Seidel iterative method are given. We also show that if the linear system of equations is consistent, then the proposed methods with a zero vector as an initial guess ...

We consider multigrid methods applied to standard linear finite element discretizations of linear elliptic boundary value problems in 2D. In the multigrid method damped Jacobi or damped Gauss-Seidel is used as a smoother. We prove that the two-grid method with v pre-smoothing iterations has a contraction number with respect to the maximum norm that is (asymptotically) bounded by Cv-~ I1n hkl 2 ...

In this paper, we develop a Jacobi-Gauss-Lobatto collocation method for solving the nonlinear fractional Langevin equation with three-point boundary conditions. The fractional derivative is described in the Caputo sense. The shifted Jacobi-Gauss-Lobatto points are used as collocation nodes. The main characteristic behind the Jacobi-Gauss-Lobatto collocation approach is that it reduces such a pr...

The finite temperature Lanczos method (FTLM), which is an exact diagonalization intensively used in quantum many-body calculations, formulated the framework of orthogonal polynomials and Gauss quadrature. main idea to reduce static dynamic quantities into weighted summations related one- two-dimensional quadratures. Then lower order quadrature, generated from iteration, can be applied approxima...

for 12386 A Comparison Theorem of the Improving Gauss-Seidel method for H-matrix and its Comparison Matrix Authors: liying Sun, xingye xu Affiliations: Math Dept.of Guangdong Education Institute, Math Dept. of Guangdong Education Institute