Abstract: Firstly the polynomial preconditioning technique and an interpolation polynomial method are considered for constructing a proper polynomial preconditioners to  transform the system.This reduces the distribution range of singular value and improves the ratio of singular value.Besides,a new algorithm is given and the convergence of the algorithm is analysed.The expression of estimation about  convergence rate testifies that this algorithm can improve the convergence rate of iterative methods significantly if  a appropriate preconditioning matrix is used.The numerical experiments show that the preconditioning matrix is more effective in convergence of algorithm than the original matrix.The superiority of the preconditioning matrix in solving speed is demonstrated.Therefore,the feasibility of the algorithm is illustrated.

Key words: matrix equation, polynomial, preconditioning technique, iterative method