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On the dimension of spaces of pp functions with boundary conditions

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Approximation Theory and its Applications

Abstract

In this paper we study the dimension of spaces of pp (piecewise polynomial) functions satisfying boundary conditions on a three direction mesh (or type-1 triangulation) and on a four direction mesh (or type-2 triangulation). The work in this area was initiated by Chui, Schumaker and Wang in [3, 4, 5].

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References

  1. De Boor, C. and Hollig, K., B-splines from Parallelepiped, J. d’ Anal. Math., 42, 1982/3, 99–115.

    Article  Google Scholar 

  2. —, Bivariate Box Splines and Smooth PP Functions on A Three Direction Mesh, J. Comput. Appl. Math., 9, 1983, 13–28.

    Article  MATH  MathSciNet  Google Scholar 

  3. Chui, C.K. and Schumaker, L.L., On Spaces of Piecewise Polynomials with Boundary Conditions I: Rectangles, Multivariate Approximation Theory II, ed. by W. Schempp and K. Zeller, Birkhauser, Basel, 1982, 69–80.

    Google Scholar 

  4. Chui, C.K., Schumaker, L.L. & Wang, R.H., On Spaces of Piecewise Polynomials wit Boundary Conditions II: Type-1 triangulation, Proceedings of the Conference on Approximation Theory, CMS conference proceedings, vol. 3, 1982, 51–66.

    MathSciNet  Google Scholar 

  5. —, On Spaces of piecewise Polynomials with Boundary Conditions III: Type-2 triangulation, Proceedings of the Conference on Approximation Theory, CMS Conference proceedings, vol. 3, 1982, 67–80.

    MathSciNet  Google Scholar 

  6. Chui, C.K. and Wang, R.H., Multivariate Spline Spaces, J. Math. Anal. Appl, 94 1983, 197–221.

    Article  MATH  MathSciNet  Google Scholar 

  7. Dahmen, W., On Multivariate B-splines, SIAM J. Numer. Anal., 17, 1980, 179–191.

    Article  MATH  MathSciNet  Google Scholar 

  8. Dahmen, W. and Micchelli, C.A., Recent Progress in Multivariate Splines Approximation Theory IV, ed. by C.K. Chui, L.L. Schumaker & J. Ward, Academic Press, New York, 1983, 27–121.

    Google Scholar 

  9. Schumaker, L.L., On Space of Piecewise Polynomials in two Variables, Approximation Theory and Spline Functions, S. P. Singh et al. eds., D. Reidel Publishing Company, Dordrecht, Holland, 1984, 151–197.

    Google Scholar 

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Authors and Affiliations

  1. Metrology College of China, China

    Le Anbo

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  1. Le Anbo
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Anbo, L. On the dimension of spaces of pp functions with boundary conditions. Approx. Theory & its Appl. 5, 19–29 (1989). https://doi.org/10.1007/BF02836066

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  • DOI: https://doi.org/10.1007/BF02836066

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