指数加权引出的几类[1/1]阶Padé逼近迭代算法

Several Classes of Index Weighted Iterative Formula Based on[1/1]PadéApproximants

函数值Padé逼近迭代算法在有理函数逼近领域具有较高的应用价值.本文利用函数值Padé逼近的[1/1]阶迭代算法,通过对非线性方程f(x)=0进行指数加权同等变形为e g(x)f(x)=0,并对加权因子g(x)进行不同类型函数赋值,得到带参数a的四类三阶收敛的迭代算法.通过收敛性分析和数值实例发现,参数a的取值并不影响收敛阶数和效率指数,而且通过调试a的变化,能够提高迭代算法的收敛速度,使其优于基础迭代,从而有效控制重根附近发散问题.研究结果显示了该迭代算法的实用性和有效性.

The function-valued Padéapproximation iterative algorithm demonstrates high application in the field of rational function approximation.On the base of the[1/1]order iterative algorithm of function-valued Padéapproximation,four types of third-order convergence iterative algorithms with parameter a are obtained by equally deforming the nonlinear equations f(x)=0 with exponential weighting to e g(x)f(x)=0 and assigning different types of functions to the weighting factors g(x).Convergence analysis and numerical examples have revealed that the value of the parameter a do not affect the convergence order and the efficiency index.Moreover,by debugging the change of a,the convergence speed of the iterative algorithm can be improved to make it better than the basic iteration,so that the divergence problem near the multiple roots can be effectively controlled.The results show the practicability and effectiveness of this iterative algorithm.