Abstract
In this paper, we are studying new approaches in numerical accuracy of the linear system of equations by successive over-relaxation method, analyzing the convergence criteria of iterative methods and comparing the SOR method with other iterative methods. We have shown SOR method converges more rapidly with the others with the help of some typical examples. All the calculations have been performed with the help of MATLAB 2020R.
Highlights
Numerical analysis is the area of mathematics and computer science that creates, analyzes, and implements algorithms for solving numerically the problems of continuous mathematics
Indirect methods are called as Iterative methods [4]
He introduced a relaxation factor to the Gauss-Seidal method to increase the rate of convergence
Summary
Numerical analysis is the area of mathematics and computer science that creates, analyzes, and implements algorithms for solving numerically the problems of continuous mathematics. The rate of converges of an iterative method depends strongly on the eigen values of the coefficient matrix A. He introduced a relaxation factor to the Gauss-Seidal method to increase the rate of convergence. The value of relaxation parameter in SOR method is not yet find for all types of system of equations. The value of relaxation parameter, lies in between 0 and 2 such that the radius of convergence of iteration matrix of SOR method, should be less than 1 (see [2, 11]).
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