Tchebyshev Approximation by $S_1^0(\Delta)$ over Some Special Triangulations
Received:March 20, 2010  Revised:May 28, 2010
Key Words: Tchebyshev approximation   bivariate splines   $S_1^0(\Delta)$.  
Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.10271022; 60373093; 60533060; 11101366; 61100130) and the Innovation Foundation of the Key Laboratory of High-Temperature Gasdynamics of Chinese Academy of Sciences.
Author NameAffiliation
Ren Hong WANG School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China 
Wei DAN School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China
School of Mathematical and Computational Sciences, Guangdong University of Business Studies, Guangdong 510320, P. R. China 
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Abstract:
      The critical point set plays a central role in the theory of Tchebyshev approximation. Generally, in multivariate Tchebyshev approximation, it is not a trivial task to determine whether a set is critical or not. In this paper, we study the characterization of the critical point set of $S_1^0(\Delta)$ in geometry, where $\Delta$ is restricted to some special triangulations (bitriangular, single road and star triangulations). Such geometrical characterization is convenient to use in the determination of a critical point set.
Citation:
DOI:10.3770/j.issn:2095-2651.2012.01.001
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