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Indexed by:期刊论文

Date of Publication:2006-10-15

Journal:International Symposium on Computing and Information

Included Journals:SCIE、EI、CPCI-S、Scopus

Volume:195

Issue:1-2,SI

Page Number:113-133

ISSN No.:0377-0427

Key Words:multivariate spline; smoothing cofactor; generator basis; structure matrix

Abstract:In this paper, we discuss the structure of multivariate spline spaces on arbitrary triangulation by using the methods and results of smoothing cofactor and generator basis of modules. On the base of analyzing the algebraic and geometric results about singularity of S1/2(Delta(MS)), we build the structure of triangulation and give some useful geometric conditions such that S-mu+1(mu)(Delta) space is singular, and we obtain an algebraic condition which is necessary and sufficient for the singularity of S-mu+1(mu)(Delta) spaces as well as their dimension formulae. Moreover, the structure matrix of spline spaces over any given partition is defined, which has been used to discuss the structure of S1/3(Delta) and S1/2(Delta) spaces over arbitrary triangulation and to prove the nonsingularity of S1/3(Delta) spaces. This partially settles a conjecture on the singularity of spline spaces in Wang et al., [Multivariate Spline and its Applications, Kluwer Press, Dordrecht, 2002; Academic Press, Beijing, 1994 (in Chinese)]. Meanwhile, the dimension formulae of S1/3(Delta), S1/2(Delta) spaces and the dimension formulae of S-mu+1(mu)(Delta)(mu >= 1) spaces are also given in this paper. (c) 2005 Elsevier B.V. All rights reserved.