Two Kinds Of Simultaneous Iterations With Five Order Convergence

With the rapid development of modern science and technology, numerical computation has become more and more important. The problem of solving polynomial equations is an indispensable part of numerical computation, which can be seen in physics, bioscience, chemistry, engineering science, computer sci-ence, control theory and so on. Due to the complexity of these problems, the polynomial equations we study tend to have the shortage of high order. Thus we can hardly solve them in direct methods. Iterative method is an efficient tool for solving polynomial equations. Simultaneous iterative method belongs to the most efficient method with the widely use of parallel digital computers.In this paper, we construct two simultaneous iterative methods of high order from different angles. The main contributions are as follows:In chapter one, the history of simultaneous iterative iterations is reviewed, and some typical methods are listed. In chapter two, starting from a simultane-ous iteration with four order convergence, we derive a new simultaneous iterative method of five order. Initial conditions and numerical examples are given. In chapter three, starting from a. single iterative formula with four order conver-gence, we also conclude another simultaneous iterative method of five order Then we give some numerical examples. In the last chapter, we make a summery of the whole paper, and make a prospect for the future.