【摘要】 应用迭代法的困难之处在于 :一是迭代公式是否存在导数运算 ;二是初始值选定是否影响迭代公式的收敛性 ;三是收敛快速和达到需要精度等问题。我们获得了求方程根不用计算导数的平方收敛迭代公式 ,并设计了求根的大范围收敛算法 ,编写了 C+ + 语言程序 ,进行了算法和数值分析。与其它算法比较 ,该算法具有无导数计算、初值任意选定、平方快速收敛、大范围收敛和双精度控制 (根的精度和函数值的精度控制 )等优点。更多还原

【Abstract】 The difficulties in using iterative algorithms lay as the following: At first, derivative feasibility; Secondly, sensitivity of iterative convergenc e to initial values; thirdly, the convergent rate and the iterative precision. T he paper presents a derivative-free iterative formula with second-order converge nt rate. Based upon it, a global convergent algorithm for the roots of equatio ns is designed using C ++ programming. The numerical analysis show that i t has several features comparing with conventional iterative algorithms, such as de rivative-free, robustness to the selection of the initial values, high convergen t rate, the global optimization and double precision control (root and function al precisions).更多还原