Second degree generalized gauss-Seidel iteration method for solving linear system of equations

Abstract

In this paper, a second degree generalized Gauss –Seidel iteration (SDGGS) method for solving linear system of equations whose iterative matrix has real and complex eigenvalues are less than unity in magnitude is presented. Few numerical examples are considered to show the efficiency of the new method compared to first degree Gauss-Seidel (GS), first degree Generalized Gauss-Seidel (GGS) and Second degree Gauss-Seidel (SDGS) methods. It is observed that the spectral radius of the new Second degree Generalized Gauss-Seidel (SDGGS) method is less than the spectral radius of the methods GS, GGS and SDGS. By use of second degree iteration (SD) method, it is possible to accelerate the convergence of any iterative method.

Key words: Gauss-Seidel method (GS); Generalized Gauss-Seidel method (GGS); Strictly Diagonally Dominant Matrix.