基于最优Rump区间算子的非线性方程组解的可信验证方法  

An Improved Verification Algorithm for Nonlinear Systems of Equations Based on the Optimal Rump Interval Operator

作　　者：姚李 侯国亮 蒋莹莹 YAO Li;HOU Guo-iang;JIANG Ying-ying(College of Mathematics,Changchun Normal University,Jilin Province,Changchun 130032,China)

机构地区：[1]长春师范大学数学学院,吉林长春130032

出　　处：《数学的实践与认识》2024年第3期88-98,共11页Mathematics in Practice and Theory

摘　　要：基于Baumann最优中心形式对Rump提出的非线性方程组解的存在性验证方法进行了改进.首先研究了Rump区间算子与Krawczyk区间算子的关系;其次借鉴最优Krawczyk区间算子的构造过程,给出了Rump区间算子的最优形式;最后根据改进的Rump解的存在性定理,设计了验证非线性方程组解存在的区间算法程序.与Rump验证算法相比,理论分析与数值实验均表明,所提算法均可以给出宽度最窄(或至少相同)的解的包含区间.In this paper,an improved verification algorithm for solutions of nonlinear systems of equations is proposed based on the Baumann optimal central form.Firstly,the relationship between the Rump interval operator and the Krawczyk interval operator is stud-ied;Secondly,the optimal Rump interval operator is given with the method of construction for the optimal Krawczyk interval operator;And finally,an interval algorithm is designed to verify the existence of solutions of nonlinear systems of equations based on the improved Rump's existence theorem for solutions.Compared with Rump's verification algorithm,both theoretical and numerical experimental results show that the algorithms given in this paper can give the inclusion intervals with the narrowest(or at least the same)width of these solutions.

关 键 词：最优Rump区间算子 Baumann最优中心形式 可信验证 

分 类 号：O241.7[理学—计算数学]