Improved Convergence Theorems for the JOR Method

Based on the concept of the doubly α-diagonal strictly dominance,a new upper bound for the spectral radius and convergence of JOR iterations are presented,aiming at commonly used JOR iteration method in solving the linear equation Ax=b.The results are suitable not only for double strictly diagonal dominant matrices,but also for doubly α-diagonal strictly dominant matrices.Assessment of the spectrum radius of the relative iteration matrix is more exact,and the range for choosing convergent parameters of JOR is extended.Finally,a numerical example is given to illustrate the advantage of the results in this study.