解非线性方程的一种新算法

A New Algorithm for Solving Non-linear Equation

将改进的迭代法和Ａｉｔｋｅｎ算法相结合，推导出一种新迭代算法并证明了新算法的收敛性和收敛阶仿真结果表明，用此算法求方程的根，收敛速度比Ａｉｔｋｅｎ算法要快，同时提高了解算精度，增加了初值的选择范围。

A new iterative algorithm is derived by combining the improved iterative algorithm with the Aitken algorithm .The performance and order of convergence are proved .The simulation results show that if using the new algorithm to solve equation,the convergence speed is faster than that with the Aitken algorithm.Besides,the iterative precision can be enhanced simultaneously and the selective range of the initial value is increased.So the algorithm is significant in solving equation.