求解非线性方程含参数的八阶迭代算法

An Eighth-Order Iterative Algorithm for Solving Nonlinear Equations with Parameters

摘要: 本文基于Steffensen迭代法和King迭代法提出了求解非线性方程的一类新的含参数八阶迭代算法，该迭代算法利用中心差分思想减少了导数值的计算，提高了效率指数，并且通过收敛性分析证明了该迭代算法的收敛阶是八阶。与其他迭代法相比，收敛阶和效率指数均有提高。最后，数值实验验证了算法的有效性和优越性。

Abstract: Based on Steffensen’s iterative method and King iterative method, a new class of eighth-order itera-tive algorithms with parameters is proposed to solve nonlinear equations, which uses the central difference idea to reduce the calculation of derivative values and improve the efficiency index, and convergence analysis proves that the convergence order of such iterative algorithms is eighth. Compared with other iteration methods, the convergence order and efficiency index are improved. Finally, numerical experiments verify the effectiveness and superiority of the algorithm.