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THE ELLIPTIC TYPE NODE CONFIGURATION AND interpolation IN R^2

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Journal of Computational Mathematics 1998年第3期16卷 257-266页

作者： Ping Zhu (Ji’an Teachers College, Ji’an 543009, Jiangxi, China) 吉安师范专科学校江西吉安 343009

In this paper, we have obtained an expression of the bivariate Vandermonde determinant for the Elliptic Type Node Configuration in R-2, and discussed the possibility of the corresponding multivariate Lagrange, Hermite... 详细信息

关键词： multivariate interpolation polynomial interpolation Birkhoff interpolation node configuration

On convergence analysis of a derivative-free trust region algorithm for constrained optimization with separable structure

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Science China Mathematics 2014年第6期57卷 1287-1302页

作者： XUE Dan SUN WenYu School of Mathematical Sciences Jiangsu Key Labratory for NSLSCSNanjing Normal University

In this paper,we propose a derivative-free trust region algorithm for constrained minimization problems with separable structure,where derivatives of the objective function are not available and cannot be directly *** each iteration,we construct a quadratic interpolation model of the objective function around the current *** new iterates are generated by minimizing the augmented Lagrangian function of this model over the trust *** filter technique is used to ensure the feasibility and optimality of the iterative *** convergence of the proposed algorithm is proved under some suitable assumptions.

关键词： constrained optimization derivative-free optimization multivariate interpolation separable op-timization global convergence

ON HIGH DIMENSIONAL interpolation

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Numerical Mathematics A Journal of Chinese Universities(English Series) 2001年第1期10卷 20-25页

作者：朱平周利华 Multimedia Technology Institute Xidian University

This paper introduces the definition of the Orthogonal Type Node Configuration and discusses the corresponding multivariate Lagrange, Hermite and Birkhoff interpolation problems in high dimensional space R s(s>2). This node configuration can be considered to be a kind of extension of the Cross Type Node Configuration , in R 2 to high dimensional spaces. And the Mixed Type Node Configuration in R s(s>2) is also discussed in this paper in an example.

关键词： multivariate interpolation node configuration multivariate Vandermonde determinant computer graphics Lagrange interpolation Hermite interpolation Birkhoff interpolation.

interpolation on Algebraic Manifold

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Northeastern Mathematical Journal 2003年第2期19卷 107-110页

作者：张树功董天冯果忱 Institute of Mathematics Jilin UniversityChangchun130012 Key Laboratry for Symmbolic Computation and Knowledge Engineering of Ministry of Educationchangchun130012 Institute of Mathematics Jilin UniversityChangchun130012 Key Laboratry for Symmbolic Computation and Knowledge Engineering of Ministry of Educationchangchun130012

In traditional researches of multivariate interpolation, people always assume that inter-polation nodes are not on any algebraic manifold of low degree; more precisely, there existsno polynomial with low degree vanish... 详细信息

关键词： algebraic manifold multivariate interpolation Grobner basis