A Modified Precondition in the Gauss-Seidel Method

Abstract

In recent years, a number of preconditioners have been applied to solve the linear systems with Gauss-Seidel method (see [1][2][3][4][5][6][7][8][9][10][11][12][13]). In this paper we use S l instead of (S + S m ) and compare with M. Morimoto's precondition [3] and H. Niki's precondition [5] to obtain better convergence rate. A numerical example is given which shows the preference of our method.

Application of Different <i>H</i>(<i>x</i>) in Homotopy Analysis Methods for Solving Systems of Linear Equations

“…Approximating the solutions of the system of linear and nonlinear equations has widespread applications in applied mathematics [1]- [11]. Many techniques including homotopy perturbation method (HPM) [12] and iterative methods [13] were suggested to search for the solution of linear systems.…”