A New Upper Bound for the Spectral Radius of Iterative Matrices

Jacobi and Gauss-Seidel iterations for solving large linear system Ax=b are studied. Based on the concept of the doubly diagonal dominance, new upper bound for the spectral radius of Jacobi and Gauss-Seidel iterations are presented. Results obtained improve the known corresponding results and are suited to extended matrices. Finally, two numerical examples are given for illustrating advantage results in this paper.