非线性方程组求解的超混沌序列最小二乘法及其应用  

Hyper-chaotic sequence least square method for solving nonlinear equations and its application

作　　者：罗佑新[1] 何哲明[1] 车晓毅[1] 

机构地区：[1]湖南文理学院机械工程学院,湖南常德415000

出　　处：《湖南文理学院学报（自然科学版）》2010年第1期36-39,共4页Journal of Hunan University of Arts and Science(Science and Technology)

基　　金：国家自然科学基金(50845038);湖南省"十一五"重点建设学科"机械设计及理论"(2006180);湖南省普通高校学科带头人(2008315);湖南省教育厅重点项目(09A067);湖南省科技计划项目(2009GK3158)

摘　　要：针对非线性方程组的求解在工程上具有广泛的实际意义,经典的数值算法如牛顿法存在其收敛性依赖于初值而实际计算中初值难确定的问题,将超混沌序列和最小二乘法结合,应用二维离散超混沌系统产生迭代初始点,提出了应用超混沌序列的最小二乘法求解非线性方程组全部实数解的新方法.测试结果表明新方法的正确性和有效性.Aimed at the widespread practical significance of solving nonlinear equations in engineering, classic numerical methods such as Newton method are highly sensitive to the initial guess, but it is difficult to find a suitable good initial guess in practical operation problem, combining least square method with hyper-chaotie sequences, hyper-chaotie sequence least square method based on utilizing two dimensional discrete hyper-chaotic system to obtain locate initial points to find all real solutions of the nonlinear questions was proposed. Experimental results show the eorrectness and validity of the novel method.

关 键 词：非线性方程组 二维离散超混沌系统 超混沌序列 最小二乘法 

分 类 号：O241.2[理学—计算数学]