一类基于克莱姆法则的避免求导的加权插值迭代算法  

A class of weighted interpolation iteration algorithm based on Cramer′s rule

作　　者：郭巧 杨兵[2] 王伟昌 GUO Qiao;YANG Bing;WANG Weichang(School of Computer and Information Technology,Anhui Vocational and Technical College,Hefei Anhui 230611;School of Intelligent Manufacturing,Anhui Vocational and Technical College,Hefei Anhui 230611;Anhui Gongbu Zhizao Industrial Technology Co.Ltd.,Hefei Anhui 231500)

机构地区：[1]安徽职业技术学院计算机与信息技术学院,安徽合肥230611 [2]安徽职业技术学院智能制造学院,安徽合肥230611 [3]安徽工布制造科技有限公司,安徽合肥231500

出　　处：《宁夏师范学院学报》2024年第4期16-25,共10页Journal of Ningxia Normal University

基　　金：2023年安徽省高校科研项目(2023AH040192);2022年度校级科研创新团队(2022xjkytd2).

摘　　要：用n次插值多项式拟合需要求导的迭代算法,构造含有n+1个未知量的线性方程组,其中前n个未知量通过加权插值的形式,并用克莱姆法则由第n+1个未知量表示,从而避免求导.收敛性分析和数值实例进一步验证该迭代算法优于牛顿迭代,在运动机器人路径轨迹优化和非线性分数阶滑模时滞控制领域具有重要意义.This article uses n th interpolating polynomial to fit an iterative algorithm that requires differentiation,and constructs a linear equation system containing n+1 unknown variables.The first n unknowns are represented by the(n+1)th unknowns using weighted interpolation and Cramer′s rule to avoid differentiation.Convergence analysis and numerical examples further validate that this iterative algorithm is superior to the Newton iteration,and has important significance in the fields of path trajectory optimization for motion robots and nonlinear fractional order sliding mode time-delay control.

关 键 词：克莱姆法则 避免求导 加权插值 迭代 

分 类 号：O241.7[理学—计算数学]