The SOR iteration for solving linear systems of equations depends upon an overrelaxation factor co. We show that, for the standard model problem of Poisson's equation on a rectangle, the optimal co and corresponding convergence rate can be obtained rigorously by Fourier analysis. The trick is to tilt the space-time grid so that the SOR stencil becomes symmetrical. The tilted grid also gives new...

In [N. Ujević, New iterative method for solving linear systems, Appl. Math. Comput. 179 (2006) 725730], a new iterative method for solving linear system of equations was presented which can be considered as a modification of the Gauss-Seidel method. Then in [Y.-F. Jing and T.-Z. Huang, On a new iterative method for solving linear systems and comparison results, J. Comput. Appl. Math., In press]...

A fast and efficient numerical method based on the Gauss-Jacobi quadrature is described that is suitable for solving Fredholm singular integral equations of the second kind that are frequently encountered in fracture and contact mechanics. Here we concentrate on the case when the unknown function is singular at both ends of the interval. Quadrature formulae involve fixed nodal points and provid...

Absrrucr: Applying Gauss-Seidel approach to the improvements of two simultaneous methods for finding polynomial zeros, presented in [9], two iterative methods with faster convergence are obtained. The lower bounds of the R-order of convergence for the accelerated methods are given. The improved methods and their accelerated modifications arc discussed in view of the convergence order and the nu...

We study some properties of the Askey-Wilson polynomials (AWP) when q is a primitive Nth root of unity. For general four-parameter AWP, zeros of the Nth polynomial and the orthogonality measure are found explicitly. Special subclasses of the AWP, e.g., the continuous q-Jacobi and big q-Jacobi polynomials, are considered in detail. A set of discrete weight functions positive on a real interval i...

In this paper an iterative technique for sequential mobile power updates in 3G WCDMA networks based on Relaxation Method has been presented. The obtained algorithm is distributed and has the same complexity as the popular DPC (distributed power control) algorithm, which is based on Gauss-Seidel iterations, and which assumes simultaneous power updates for all mobiles that use the same frequency ...

Multigrid (MG) methods are used to approximate solutions to elliptic partial differential equations (PDEs) by iteratively improving the solution through a sequence of coarser discretizations or grids. The methodology has been developed and extended since the 1970’s to also target more general PDEs and systems of algebraic equations. A typical approach consists of a series of refinements or grid...

diffusion equations using a nine-point compact difference scheme. implementation with multigrid, and carry out a Fourier We test the efficiency of the algorithm with various smoothers and smoothing analysis of the Gauss–Seidel operator. In Secintergrid transfer operators. The algorithm displays a grid-indepention 3 we present numerical experiments that demonstrate dent convergence rate and prod...

A twocolor Fourier analytical approach is proposed to analyze the multigrid method which employs the red-black Gauss-Seidel smoothing iteration for solving the Poisson equation. In this approach, Fourier components in the high-frequency region are folded into the low-frequency region so that the coupling between the low and high Fourier components is transformed into a coupling between componen...

A number of conservative PDEs, like various wave equations, allow for a multi-symplectic formulation which can be viewed as a generalization of the symplectic structure of Hamiltonian ODEs. We show that Gauss-Legendre collocation in space and time leads to multi-symplectic integrators, i.e., to numerical methods that preserve a symplectic conservation law similar to the conservation of symplect...