期刊文献+
任意字段
题名或关键词
题名
关键词
文摘
作者
第一作者
机构
刊名
分类号
参考文献
作者简介
基金资助
栏目信息

一个全局隐函数定理及计算隐函数的迭代算法 被引量：1

A Global Implicit Function Theorem and the Iterative Algorithms of Counting the Implicit Function
在线阅读 下载PDF
导出
摘要 利用Banach压缩映射原理,证明了高维空间中的一个全局隐函数定理,给出计算隐函数近似解的迭代算法,并证明迭代序列收敛于隐函数的精确解,改进和推广了某些文献中已知的结果. In this paper, by using the Banach contraction mapping principle, we prove a global implicit function theorem in high dimension space, and give some iterative algorithms of counting the approximation of the implicit function. We also prove that the iterative sequence tends to the exact solution of the implicit function. The present results improve and generalize some known ones in the literature.
作者 陈渝 罗春林
机构地区 康定民族师范专科学校数学系
出处 《四川师范大学学报（自然科学版）》 CAS CSCD 北大核心 2008年第3期316-319,共4页 Journal of Sichuan Normal University（Natural Science）
基金 四川省教育厅自然科学重点基金(2003A186)资助项目
关键词 全局隐函数 全局存在性 迭代算法 Global implicit function Global existence Iterative algorithms
分类号 O177 [理学—基础数学] O178 [理学—基础数学]
  • 相关文献

参考文献16

  • 1Bridges D, Calude C, Pavlov B, et al. Chaos Solitons Fractals ,1999 ,10 :927-934.
  • 2Datko R. An implicit function theorem with an application to control theory [ J ]. Michigan Math J, 1964,11:345-351.
  • 3Ge S S, Hang C C, Zhang T. Nonlinear adaptive control using neural networks and its application to CSTR systems[ J]. J Process Control, 1999,9:313-323.
  • 4Ge S S, Hang C C, Zhang T. Adaptive neural network control of nonlinear systems by state and output feedback[ J ]. IEEE Trans Syst Man Cybernetics Part B ,1999,29:818-828.
  • 5Ge S S, Hang C C, Lee T H, et al. Stable Adaptive Neural Network Control[M]. Boston:Kluwer Academic,2001.
  • 6Jittorntrum K. An implicit function theorem [ J ]. J Optim Theory Appl, 1978,25:575-577.
  • 7Alexandrov V. Implicit function theorem for systems of polynomial equations with vanishing Jacobian and its application to flexible polyhedra and frameworks [ J ]. Monatsh Math ,2001,132:269-288.
  • 8Butler G J, Freedman H I. Further critical cases of the scalar implicit function theorem[ J]. Aequationes Math ,1972,8:203-211.
  • 9Craven B D, Nashed M Z. Generalized implicit function theorems when the derivative has no bounded inverse [ J ]. Nonlinear Anal, 1982,6:375-387.
  • 10Pales Z. Inverse and implicit function theorems for nonsmooth maps in Banach spaces[J]. J Math Anal Appl ,1997 ,209 :202-220.

二级参考文献33

  • 1叶明露,邓方平.一般变分不等式的超梯度算法[J].四川师范大学学报（自然科学版）,2005,28(3):265-269. 被引量：4
  • 2Bertsekas D P, Tsitsiklis J. Parallel and Distributed Computation Numerical Methods[ M]. New Jersey: Prentice Hall, 1989.
  • 3Han D, Lo H K. Two new self-adaptive projection methods for variational inequality problems[J]. Computer and Mathematics with Applications,2002,43:1529 ～ 1537.
  • 4He B S, Liao L Z. Improvement of some projection methods for monotone nonlinear variational inequalities[ J ]. Journal of Optimization Theory and Applications, 2002,112:111 ～ 128.
  • 5Noor M A. Some recent advances in variational inequalities, part 1: basic concepts[ J]. New Zealand Journal of Mathematics, 1997,26:53～80.
  • 6Noor M A. Some recent advances in variational inequalities, part2: other concepts[ J]. New Zealand Journal of Mathematics, 1997,26:229～ 255.
  • 7Iusem A N, Svaiter B F. A various of Korpelevich's method for variational inequalities with a new search strategy[ J]. Optimization, 1997,42:309～ 321.
  • 8Noor M A. Some algorithm for general monotone mixed variational inequalities[ J]. Mathematics with Computer Modeling, 1999,29:1 ～ 9.
  • 9Noor M A. A modified extragradient method for general monotone variational inequalities[ J]. Computers and Mathematics with Applications, 1999,38:19 ～ 24.
  • 10He B S. A class of projection and contraction methods for monotone variational inequalities[ J]. Application Math Optimization, 1997,35:69 ～ 76.

共引文献31

同被引文献8

引证文献1

二级引证文献2

四川师范大学学报（自然科学版）
2008年 第3期

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部