ON GENERALIZED JACOBI-TYPE AND GAUSS-SEIDEL-TYPE ITERATION METHODS FOR MATRIX EQUATION A X B= C

Abstract

In 2016, Tian et.al proposed Jacobi and Gauss-Seidel-type iteration method for solving the matrix equation A X B = C.

To explore much more effective methods for solving this matrix equation, we construct the so-called Generalized Jacobi-type and Gauss-Seidel-type methods by applying the generalization of traditional Jacobi and Gauss-Seidel methods which Salkuyeh introduced in 2007. Meanwhile, we examine their convergence requirements for different coefficient matrices, such as the M-matrix, H-matrix, and Z-matrix, to ensure that this generalization of splitting structure is practical in iterative methods.

Numerous numerical examples and their solutions will be performed to indicate the effectiveness of the Generalized Jacobi-type and Gauss-Seidel-type methods, the Modified Generalized Jacobi-type and Gauss-Seidel-type methods converge with various matrices and m.