ON DIMENSION AND EXISTENCE OF LOCAL BASES FOR MULTIVARIATE SPLINE SPACES

被引：25

作者：

ALFELD, P ^{[1
]}

SCHUMAKER, LL ^{[1
]}

SIRVENT, M ^{[1
]}

机构：

[1] VANDERBILT UNIV,DEPT MATH,NASHVILLE,TN 37235

来源：

JOURNAL OF APPROXIMATION THEORY | 1992年 / 70卷 / 02期

关键词：

D O I：

10.1016/0021-9045(92)90087-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider spaces of splines in k variables of smoothness r and degree d defined on a polytope in Rk which has been divided into simplices. Bernstein-Bézier methods are used to develop a framework for analyzing dimension and basis questions. Dimension formulae and local bases are found for the case r = 0 and general k. The main result of the paper shows the existence of local bases for spaces of trivariate splines (where k = 3) whenever d > 8r. © 1992.

引用

页码：243 / 264

页数：22

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