This paper describes our work in solving path planning problem for mobile robot by using harmonic functions to generate path in the configuration space. Harmonic functions are known to have an advantage as a global potential function in the potential field based approach for robot path planning. However, an immense amount of computations are required as the size of the environment get bigger. T...

A computationally efficient numerical method for the solution of nonlinear sea ice dynamics models employing viscous-plastic rheologies is presented. The method is based on a semi-implicit decoupling of the x and y ice momentum equations into a form having better convergence properties than the coupled equations. While this decoupled form also speeds up solutions employing point relaxation meth...

Waveform relaxation is a numerical method for solving large-scale systems of ordinary differential equations on parallel computers. It differs from standard iterative methods in that it computes the solution on many time levels or along a continuous time interval simultaneously. This paper deals with the acceleration of the standard waveform relaxation method by successive overrelaxation (SOR) ...

The vast majority of recent advances in the field of numerical radiative transfer relies on approximate operator methods better known in astrophysics as Accelerated Lambda-Iteration (ALI). A superior class of iterative schemes, in term of rates of convergence, such as Gauss-Seidel and Successive Overrelaxation methods were therefore quite naturally introduced in the field of radiative transfer ...

This paper proposed fast Half-Sweep SOR via Nine-Point Laplacian (HSSOR9L) iterative method for solving path planning problem for a mobile robot operating in indoor environment model. It is based on the use of Laplace’s Equation to constraint the distribution of potential values in the environment of the robot. Fast computation with half-sweep iteration is obtained by considering only half of w...

Suppose that A E (]J',n is a block p-cyclic consistently ordered matrix and let Band Sw denote , respectively, the black Jacobi and the block Symmetric Successive Overrelaxation (SSOR) iteration matrices associated with A. Neumaier a.nd Varga found (in the (p(IBI),w)-plane) the exact convergence and divergence domains of the SSOR method for the class of H-matrice8. Hadjidimos and Neumann applie...

A preconditioned SSOR iterative method with a multi-parameters preconditioner I + S̃α is proposed. Some convergence and comparison results for αi ∈ [0, 1] are given when the coefficient matrix of linear system A is a nonsingular M−matrix. Numerical example shows that our methods are superior to the basic SSOR iterative method.

This paper describes a method for the numerical solution of linear systems of equations. The method is a two-parameter generalization of the Successive Overrelaxation (SOR) method such that when the two parameters involved are equal it coincides with the SOR method. Finally, a numerical example is given to show the superiority of the new method.

The discretization of the two-dimensional convection-diffusion equation usually leads to a linear system whose matrix coefficient is block two-cyclic consistently ordered. For the solution of the resulting linear system, several efficient stationary iterative methods were proposed, among others, by Chin and Manteuffel (1988), Elman and Golub (1990), de Pillis (1991) and Eiermann, Niethammer and...