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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. 181-208. ISSN 1432-0940

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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 Hermite-type 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 near-degenerate 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 quasi-interpolation 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
    Subjects: Science > Mathematics > Probabilities. Mathematical statistics
    Department: Faculty of Science > Mathematics and Statistics
    Related URLs:
      Depositing user: Pure Administrator
      Date Deposited: 12 Jan 2012 12:18
      Last modified: 05 Oct 2012 08:04
      URI: http://strathprints.strath.ac.uk/id/eprint/36669

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