Error bounds for minimal energy bivariate polynomial splines

被引:18
作者
von Golitschek, M [1 ]
Lai, MJ
Schumaker, LL
机构
[1] Univ Wurzburg, Inst Angew Math & Stat, D-97074 Wurzburg, Germany
[2] Univ Georgia, Dept Math, Athens, GA 30602 USA
[3] Vanderbilt Univ, Dept Math, Nashville, TN 37240 USA
关键词
D O I
10.1007/s002110100381
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We derive error bounds for bivariate spline interpolants which are calculated by minimizing certain natural energy norms.
引用
收藏
页码:315 / 331
页数:17
相关论文
共 17 条
[1]   BOUNDS FOR A CLASS OF LINEAR FUNCTIONALS WITH APPLICATIONS TO HERMITE INTERPOLATION [J].
BRAMBLE, JH ;
HILBERT, SR .
NUMERISCHE MATHEMATIK, 1971, 16 (04) :362-&
[2]   STABILITY OF OPTIMAL-ORDER APPROXIMATION BY BIVARIATE SPLINES OVER ARBITRARY TRIANGULATIONS [J].
CHUI, CK ;
HONG, D ;
JIA, RQ .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1995, 347 (09) :3301-3318
[3]  
Davydov O, 2002, CONSTR APPROX, V18, P87
[4]  
DESILANES MCL, 1988, NUMER MATH, V53, P367
[5]   STABILITY IN LQ OF L2-PROJECTION INTO FINITE-ELEMENT FUNCTION SPACES [J].
DOUGLAS, J ;
DUPONT, T ;
WAHLBIN, L .
NUMERISCHE MATHEMATIK, 1974, 23 (03) :193-197
[6]  
FARMER KW, 1988, APPROXIMATION THEORY, V2, P47
[7]   Minimal energy surfaces using parametric splines [J].
Fasshauer, GE ;
Schumaker, LL .
COMPUTER AIDED GEOMETRIC DESIGN, 1996, 13 (01) :45-79
[8]   SCATTERED DATA INTERPOLATION AND APPROXIMATION WITH ERROR BOUNDS. [J].
Foley, Thomas A. .
Computer Aided Geometric Design, 1986, 3 (03) :163-177
[9]   SCATTERED DATA INTERPOLATION - TESTS OF SOME METHODS [J].
FRANKE, R .
MATHEMATICS OF COMPUTATION, 1982, 38 (157) :181-200
[10]   Smooth interpolation to scattered data by bivariate piecewise polynomials of odd degree [J].
Meyling, R.H.J.Gmelig ;
Pfluger, P.R. .
Computer Aided Geometric Design, 1990, 7 (05) :439-458