Masataka Usui

TL;DR: This paper uses the preconditioning matrix I + S(α) to show that if a coefficient matrix A is an irreducibly diagonally dominant Z-matrix, then [I + S (α)]A is also a strictly diagonal dominant Z -matrix and is shown that the proposed method is also superior to other iterative methods.

TL;DR: This work extends the modified Gauss-Seidel method introduced by A. D. Gunawardena et al. and shows that this method is able to improve the rate of convergence compared to the modifiedGauss- Seidel method.

TL;DR: The Practical SOR method is applied to a preconditioning method and the adaptive Gauss-Seidel method is proposed which is a precondsitioned iterative method.

TL;DR: This work extends the adaptive Gauss-Seidel method to a multi-step preconditioning method and finds that this method yields a superior rate of the convergence than the adaptiveGauss- Seidel method.