基于有界变量单纯形法的改进区间牛顿法  

Improved interval Newton algorithm based on the bounded simplex method

作　　者：陈利民[1] 苏宏业[1] 牟盛静[1] 褚健[1] 

机构地区：[1]浙江大学先进控制研究所,浙江杭州310027

出　　处：《浙江大学学报（工学版）》2003年第3期269-272,287,共5页Journal of Zhejiang University：Engineering Science

基　　金：国家自然科学基金资助项目(60025308).

摘　　要：提出使用有界变量单纯形法来改进区间牛顿法.首先将非线性问题转化为带约束条件的线性规划问题,该线性规划的可行域包含了所给区间向量范围内的所有解,然后使用有界变量的单纯形法判断可行域是否为空.若可行域为空,则可排除该区间向量.结果表明,该改进算法可大大减少迭代次数和计算时间.The computation cost of Interval Newton algorithm is higher than that of the general Newton iteration method. Here the simplex method was applied to improve the Interval Newton algorithm. The nonlinear equations were first transformed into a linear programming problem whose feasible region contained all solutions in the given interval vector; then the simplex method was used to determine whether the feasible region was empty or not. If the feasible region was empty, the interval vector can be excluded. Results indicate that the iteration times and computation time can be substantially reduced. 

关 键 词：非线性方程组 线性规划 有界变量 单纯形法 改进区间牛顿法 迭代次数 

分 类 号：O221.1[理学—运筹学与控制论] O242.23[理学—数学]