Bivariate spline interpolation with optimal approximation order
Davydov, Oleg and Nurnberger, G. and Zeilfelder, F. (2001) Bivariate spline interpolation with optimal approximation order. Constructive Approximation, 17 (2). pp. 181208.

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Abstract
Let be a triangulation of some polygonal domain f c R2 and let S9 (A) denote the space of all bivariate polynomial splines of smoothness r and degree q with respect to A. We develop the first Hermitetype interpolation scheme for S9 (A), q >_ 3r + 2, whose approximation error is bounded above by Kh4+i, where h is the maximal diameter of the triangles in A, and the constant K only depends on the smallest angle of the triangulation and is independent of neardegenerate edges and nearsingular vertices. Moreover, the fundamental functions of our scheme are minimally supported and form a locally linearly independent basis for a superspline subspace of Sr, (A). This shows that the optimal approximation order can be achieved by using minimally supported splines. Our method of proof is completely different from the quasiinterpolation techniques for the study of the approximation power of bivariate splines developed in [71 and [181.
Item type:  Article 

ID code:  36669 
Keywords:  bivariate spline interpolation , optimal approximation, mathematical analysis, Probabilities. Mathematical statistics, Computational Mathematics, Analysis, Mathematics(all) 
Subjects:  Science > Mathematics > Probabilities. Mathematical statistics 
Department:  Faculty of Science > Mathematics and Statistics 
Depositing user:  Pure Administrator 
Date Deposited:  12 Jan 2012 12:18 
Last modified:  28 Apr 2016 10:49 
URI:  http://strathprints.strath.ac.uk/id/eprint/36669 