AN EXTENDED CONTINUOUS NEWTON METHOD

被引:22
|
作者
DIENER, I
SCHABACK, R
机构
[1] Institute for Numerical and Applied Mathematics, University of Göttingen, Göttingen
关键词
continuous Newton method; critical points; Global optimization; multiple solutions; trajectory method;
D O I
10.1007/BF00939735
中图分类号
C93 [管理学]; O22 [运筹学];
学科分类号
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要
This paper describes a numerical realization of an extended continuous Newton method defined by Diener. It traces a connected set of locally one-dimensional trajectories which contains all critical points of a smooth function f:ℝn→ℝ. The results show that the method is effectively applicable. © 1990 Plenum Publishing Corporation.
引用
收藏
页码:57 / 77
页数:21
相关论文
共 50 条
  • [1] On the extended Newton's method
    Berinde, V
    ADVANCES IN DIFFERENCE EQUATIONS-BOOK, 1997, : 81 - 88
  • [2] Continuous Newton's Method
    Neuberger, J. W.
    SOBOLEV GRADIENTS AND DIFFERENTIAL EQUATIONS, SECOND EDITION, 2010, 1670 : 79 - 83
  • [3] On the Convergence Rate of the Continuous Newton Method
    Gibali A.
    Shoikhet D.
    Tarkhanov N.
    Journal of Mathematical Sciences, 2019, 239 (6) : 867 - 879
  • [4] Weak singularities and the continuous Newton method
    Riaza, R
    Zufiria, PJ
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1999, 236 (02) : 438 - 462
  • [5] Newton's method for ω-continuous semirings
    Esparza, Javier
    Kiefer, Stefan
    Luttenberger, Michael
    AUTOMATA, LANGUAGES AND PROGRAMMING, PT 2, PROCEEDINGS, 2008, 5126 : 14 - 26
  • [6] Continuous newton’s method for polynomials
    J. W. Neuberger
    The Mathematical Intelligencer, 1999, 21 : 18 - 23
  • [7] Continuous Newton's method for polynomials
    Neuberger, JW
    MATHEMATICAL INTELLIGENCER, 1999, 21 (03): : 18 - 23
  • [8] An acceleration of the continuous Newton's method
    Gutierrez, J. M.
    Hernandez-Veron, M. A.
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2019, 354 : 213 - 220
  • [9] REGULARIZED VERSIONS OF CONTINUOUS NEWTON'S METHOD AND CONTINUOUS MODIFIED NEWTON'S METHOD UNDER GENERAL SOURCE CONDITIONS
    Nair, M. T.
    Ravishankar, P.
    NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2008, 29 (9-10) : 1140 - 1165
  • [10] Continuous analog of the Gauss-Newton method
    Airapetyan, RG
    Ramm, AG
    Smirnova, AB
    MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 1999, 9 (03): : 463 - 474