A Practical Algorithm For Finding Optimal Relaxation Factor

In this paper,we discuss a practical algorithm for finding optimal relax-ation factor,This algorithm can be described as follows,the compatible ordi-nal matrix is single mount function within interval[1,2] .so we can use 0.618method to approximate the optimal value, firstly,we try computing with twotesting points to decide the next iteration interval.Then we can use the sameway to look for the interval satisfying the condition given by the question,so,any points within the interval can be looked on as the optimal relaxationfactor.As a rule, the testing points is looked on as relaxation factor,We discuss convergence rate of the three iteration method,and how tojudge wether a matrix is a compatible ordinal matrix or not .At last ,we give some numerical examples to indicate that the new ideais something useful and helpful.