Improving the modified Gauss-Seidel method for Z-matrices

Valuing option on the maximum of two assets using improving modified Gauss-Seidel method

“…The IMGS method can be formulated by multiply both sides of the linear system in (9) with a preconditioned matrix [8]. Then, the linear system can be rewritten as,…”

“…If 0 , it is the standard Gauss-Seidel (GS) method, whereas if 1 , it is the MGS method. For IMGS method, the can be selected by numerical simulation [8].…”

“…Jeong et al [2] applied a numerical approach, namely the Multigrid method to solve a two asset option pricing, but on different style of option which is the two assets cash or nothing call option. Nevertheless, we would like to study on the preconditioned iterative method established by Kohno et al [8] that is the Improving Modified GaussSeidel (IMGS) iterative method, in solving the option on the maximum of two assets. In fact, Kohno et al [8] improved on the Modified Gauss-Seidel (MGS) iterative method [9], by introducing a parameter in the preconditioned matrix.…”

“…Nevertheless, we would like to study on the preconditioned iterative method established by Kohno et al [8] that is the Improving Modified GaussSeidel (IMGS) iterative method, in solving the option on the maximum of two assets. In fact, Kohno et al [8] improved on the Modified Gauss-Seidel (MGS) iterative method [9], by introducing a parameter in the preconditioned matrix. Subsequently, IMGS method had been applied in solving European put option and had shown to be superior to MGS and GS methods [10].…”

A Modified Precondition in the Gauss-Seidel Method

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ABSTRACTIn 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.

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