Padé逼近引出的[1/n]阶加权迭代算法

An Weighted Iterative Formula Based on[1/n]PadéApproximants

在有理函数逼近领域,Padé逼近是比较经典的求解非线性方程及方程组根的算法.本文以[1/0]、[1/1]、[1/2]阶Padé逼近所构造的迭代算法为基础,通过增加指数权重,进行泰勒级数展开,得到三类带参数的迭代算法,并进行收敛性分析,通过数值实例验证,在参数值特定情况下得到的迭代公式收敛速度优于Padé逼近,并且能够有效控制重根附近发散的情况,该算法在工程计算中的实用价值更突出.

In the field of rational function approximation,Padéapproximation is a classical algorithm for finding the roots of nonlinear equations or systems of equations.In this paper,based on the iterative algorithms constructed by Padéapproximation of[1/0],[1/1]and[1/2]order,three types of iterative algorithms with parameters are obtained and convergence analysis is performed by increasing the exponential weights and applying Taylor series expansion.It is verified by numerical examples that the iterative formulas obtained for specific values of parameters converge is faster than the Padéapproximation and can effectively control the divergence around the repeated roots.The algorithm is more valuable in engineering calculations.