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Spaces of bivariate spline functions over triangulation

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Approximation Theory and its Applications

Abstract

We consider the spaces of bivariate Cμ-splines of degree k defined over arbitrary triangulations of a polygonal domain. We get an explicit formula for the dimension of such spaces when k≥3μ+2 and construct a local basis for them. The dimension formula is valid for any polygonal domain even it is complex connected, and the formula is sharp since it evaluates the lower-bound which was given by Schumaker in [11].

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Authors and Affiliations

  1. Department of Mathematics, Texas A & M University, 77843, College Station, Texas, U.S.A.

    Hong Dong

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  1. Hong Dong
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Additional information

The author wishes to thank sincerely professor Rongqing Jia for his encouragement and advice in [3]. For μ≥2, the question is still open.

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Dong, H. Spaces of bivariate spline functions over triangulation. Approx. Theory & its Appl. 7, 56–75 (1991). https://doi.org/10.1007/BF02907546

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  • DOI: https://doi.org/10.1007/BF02907546

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