# The Modified Successive Overrelaxation Method with Fixed Parameters

@article{Kincaid1972TheMS, title={The Modified Successive Overrelaxation Method with Fixed Parameters}, author={David R. Kincaid and David M. Young}, journal={Mathematics of Computation}, year={1972}, volume={26}, pages={705-717} }

Expressions for the spectral radius and for certain norms of the modified successive overrelaxation method with fixed parameters are derived. Also established are expressions for the virtual spectral radius and for certain virtual norms of this method. Parameter restrictions are determined so that the spectral radius and the norms coincide with the virtual spectral radius and the virtual norms, respectively. Optimum parameters which minimize these expressions are obtained. These results extend…

## Figures from this paper

## 24 Citations

On the modified successive overrelaxation method

- MathematicsAppl. Math. Comput.
- 2013

Convergence analysis of the modified sor (MSOR) method

- MathematicsInt. J. Comput. Math.
- 1990

The optimum parameters and the optimum virtual spectral radius of the MSOR method are obtained and a comparison of the optimum MSOR with the optimum SOR and AOR methods is made, showing the superiority of MSOR.

The application of successive overrelaxation method for the solution of linearized half-sweep finite difference approximation to two-dimensional porous medium equation

- Computer Science
- 2021

The numerical experiment that uses this innovative numerical method to solve several two-dimensional porous medium equation problems shows significant improvement to the percentage of reduction in the number of iterations and computation time.

Numerical solution of helmholtz equation using a new four point EGMSOR iterative method.

- Mathematics
- 2010

Recently, a family of block iterative method via Explicit Group (EG) iterative methods is shown to be one of the feasible and successful classes of iterative methods in solving any system of linear…

Preconditioners for Inhomogeneous Anisotropic Problems with Spherical Geometry in Ocean Modelling

- Computer Science
- 2004

Numerical evidence is presented, using a 2D spherical domain model and a standard five-point discretisation scheme, to show that the polar convergence problem is caused by the increased importance, with increased mesh anisotropy, of eigenmodes with strong polar signals.

THE SOLUTION OF 2D ELLIPTIC EQUATION USING MODIFIED GEOMETRIC MEAN METHOD ON SKEWED GRID WITH RED-BLACK ORDERING

- Computer Science
- 2021

The developed SkMGM scheme is compared with the other methods on the standard grid to confirm the effectiveness of the proposed method in terms of computational complexity and execution time.

Application of Four-Point Newton-EGSOR iteration for the numerical solution of 2D Porous Medium Equations

- Mathematics
- 2017

Partial differential equations that are used in describing the nonlinear heat and mass transfer phenomena are difficult to be solved. For the case where the exact solution is difficult to be…

Application of MSOR iteration with Newton scheme for solutions of 1D nonlinear porous medium equations

- Mathematics, Engineering
- 2016

This paper considers Newton-MSOR iterative method for solving 1D nonlinear porous medium equation (PME). The basic concept of proposed iterative method is derived from a combination of one step…

Autonomous Vehicle Navigation Using Harmonic Functions via Modified Arithmetic Mean Iterative Method

- Mathematics
- 2019

Harmonic functions are solutions to Laplace’s equation that are known to have an advantage as a global approach in providing the potential values for autonomous vehicle navigation. However, the…

## References

SHOWING 1-10 OF 20 REFERENCES

Convergence Properties of the Symmetric and Unsymmetric Successive Overrelaxation Methods and Related Methods

- Mathematics
- 1970

The paper is concerned with variants of the successive overrelaxation method (SOR method) for solving the linear system Au = b. Necessary and sufficient conditions are given for the convergence of…

NORMS OF THE SUCCESSIVE OVERRELAXATION METHOD AND RELATED METHODS.

- Computer Science
- 1969

Norms of several iterative methods for solving the linear system Au = b are developed and it is indicated that by using a different norm than was previously considered, the successive overrelaxation method compares more favorably with the cyclic Chebyshev semi-iterative and with the other iterative Methods considered.

A generalisation of systematic relaxation methods for consistently ordered matrices

- Computer Science
- 1969

The systematic relaxation method is analysed for consistently ordered matrices as defined by Broyden (1964) and has a better asymptotic rate of convergence than S.O.R. and requires less calculations and computer store.

Coupled harmonic equations, SOR, and Chebyshev acceleration

- Mathematics
- 1972

A coupled pair of harmonic equations is solved by the application of Chebyshev acceleration to the Jacobi, Gauss-Seidel, and related iterative methods, where the Jacobi iteration matrix has purely…

A class of norms of iterative methods for solving systems of linear equations

- Mathematics
- 1972

A new class of norms which generalize norms previously investigated by Young [9, 14], Sheldon [4, 5], Golub [1], Golub and Varga [2], Varga [6], Wachspress [7], Young and Kincaid [12], Young [14],…

Iterative Solution of Large Linear Systems.

- Mathematics
- 1971

The ASM preconditioner B is characterized by three parameters: C0, ρ(E) , and ω , which enter via assumptions on the subspaces Vi and the bilinear forms ai(·, ·) (the approximate local problems).

Solving the Biharmonic Equation as Coupled Finite Difference Equations

- Mathematics
- 1971

A technique is proposed for solving the finite difference biharmonic equation as a coupled pair of harmonic difference equations. Essentially, the method is a general block SOR method with…

An Analysis of a Class of Norms of Iterative Methods for Systems of Linear Equations

- Ph.D. Dissertation, University of Texas at Austin,
- 1971

Ehrlich , " Solving the biharmonic equation as coupled finite difference equations , " SI AM I

- Numer . Anal .
- 1971

License or copyright restrictions may apply to redistribution

- 1971