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A remark on interpolation by bivariate splines

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Approximation Theory and its Applications

Abstract

We study the determining set for bivariate spline spacesS ok on type-1 triangulation of square using B-net techniques. We further construct the interpolation schemes for these spline spaces that are unisolvent for any function f of Cσ.

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References

  1. Alfreld, P. and Schumaker, L. L., The Dimension of Bivariate Spline Spaces of Smoothness r for Degree d≥4r+1, Constr. Approx. 3 (1987), 189–197.

    Article  MathSciNet  Google Scholar 

  2. Alfreld, P., Piper, B. and Schumaker, L. L., Minimally Supported Bases for Spaces of Bivariate Piecewise Polynomials of Smoothness r and Degree d≥4r+1, Computer Aided Geometric Design 4(1987), 105–123.

    Article  MathSciNet  Google Scholar 

  3. de Boor, C. and Hollig, K., Bivariate Box Splines and Smooth pp Functions on a Three Direction Mesh, J. Comp. Math. and Appl. Math. 9(1983), 13–28.

    Article  MATH  Google Scholar 

  4. Farin, G., Triangular Bérstein-Bezier Patches, Computer Aided Geometric Design 3(1986), 83–128.

    Article  MathSciNet  Google Scholar 

  5. Gao, J. B., Interpolation by C1 Quartic Bicariate Splines, to appear in J. of Math. Res. and Exp.

  6. Gao, J. B. and Xu, L. Z., Concerning a Problem of Interpolation by Splines ofS 13 (Δ (1)mn ) Chinese Univ. J. of Comp. Math. 10(1988), 55–67.

    MATH  MathSciNet  Google Scholar 

  7. Wang, R. H., The Dimension and Basis of Spaces of Multivariate Splines, J. Comp. and Appl. Math. 12&13 (1985), 163–177.

    Article  Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematical Sciences, Dalian University of Technology, 116023, Dalian, P. R. China

    Gao Junbin

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  1. Gao Junbin
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Junbin, G. A remark on interpolation by bivariate splines. Approx. Theory & its Appl. 7, 41–50 (1991). https://doi.org/10.1007/BF02845190

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  • DOI: https://doi.org/10.1007/BF02845190

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