Padé逼近引出的[1/n]阶加权迭代算法  

An Weighted Iterative Formula Based on [1/n] Padé Approximants

作　　者：郭巧 杨兵[1] 吴昌广 GUO Qiao;YANG Bing;WU Changguang(Anhui Vocational and Technical College,Hefei 230611,China;Nanjing University of Science and Technology,Nanjing 210094,China)

机构地区：[1]安徽职业技术学院,安徽合肥230611 [2]南京理工大学,江苏南京210094

出　　处：《长春师范大学学报》2024年第8期40-45,共6页Journal of Changchun Normal University

基　　金：全国现代职业教育科教融汇课题(重点)“科教融汇视域下职业院校数学类课程数字化转型路径研究”(KJ2024Z0019);安徽省高校科学研究项目“基于机器视觉的数字孪生焊接机器人结构优化及控制算法研究”(2023AH051443);安徽省社会科学创新发展研究课题“安徽高校毕业生‘慢就业’问题研究”(2023CX160);中国高等教育学会高等教育科学研究规划课题“产教融合促进高质量就业创业的实践创新研究”(22CJRH0302)。

摘　　要：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.

关 键 词：PADÉ逼近 加权 收敛性分析 迭代算法 

分 类 号：O241.7[理学—计算数学]