超定非线性系统奇异解的可信验证

吉林大学学报(理学版)

超定非线性系统奇异解的可信验证

桑海风^1,2, 万保成^2,3

1. 北华大学数学与统计学院, 吉林吉林 132013; 2. 吉林大学数学学院, 长春 130012;3. 吉林农业大学信息技术学院, 长春 130118

收稿日期:2014-02-07 出版日期:2014-11-26 发布日期:2014-12-11
通讯作者: 万保成 E-mail:wanbaocheng@163.com

Verified Methods of Singular Solutions of Overdetermined Nonlinear Systems

SANG Haifeng^1,2, WAN Baocheng^2,3

1. College of Mathematics and Statistics, Beihua University, Jilin 132013, Jilin Province, China;2. College of Mathematics, Jilin University, Changchun 130012, China;3. College of Information Technology, Jilin Agricultural University, Changchun 130118, China

Received:2014-02-07 Online:2014-11-26 Published:2014-12-11
Contact: WAN Baocheng E-mail:wanbaocheng@163.com

摘要/Abstract

摘要：

利用边界矩阵和区间算法理论, 讨论超定系统奇异解的数值解法及其可信验证. 提出一种新算法, 该算法输出一个近似解及其相应的误差界, 使得在近似解的误差界范围内必存在一个精确解.

关键词: 超定非线性系统, 可信误差界, 奇异解

Abstract:

We studied the numerical method and verification for singular points of overdetermined nonlinear equations. And we proposed an algorithm on the basis of the bordered system and interval theory. It outputs an approximate solution and its error bound so as to make an exact solution exist within this computed bounds.

Key words: overdetermined nonlinear system, verified error bound, singular solution

中图分类号:

O242.29

桑海风, 万保成. 超定非线性系统奇异解的可信验证[J]. 吉林大学学报(理学版), 2014, 52(06): 1162-1166.

SANG Haifeng, WAN Baocheng. Verified Methods of Singular Solutions of Overdetermined Nonlinear Systems[J]. Journal of Jilin University Science Edition, 2014, 52(06): 1162-1166.

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