METODE GAUSS-SEIDEL PREKONDISI DENGAN MENGGUNAKAN EKSPANSI NEUMANN

Abstract

We discuss a preconditioned Gauss-Seidel method to solve a system of linear equation Ax = b by A which is a strictly diagonally dominant Z-matrix. Preconditioning matrix to be used is P = (I +U) −1 , where I is an identity matrix and U is a strictly upper triangular matrix. Using Neumann’s expansion to approximate P, we show
that the preconditioning matrix is equivalent to an existing preconditioning matrix of the form P = (I + βU). Numerical computations show that the proposed preconditioned
Gauss-Seidel method is better than the standard Gauss-Seidel method in solving a system of linear equation Ax = b.