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Computing quasi-interpolants from the B-form of B-splines

Author

Listed:
  • Abbadi, A.
  • Ibáñez, M.J.
  • Sbibih, D.

Abstract

In general, for a sufficiently regular function, an expression for the quasi-interpolation error associated with discrete, differential and integral quasi-interpolants can be derived involving a term measuring how well the non-reproduced monomials are approximated. That term depends on some expressions of the coefficients defining the quasi-interpolant, and its minimization has been proposed. However, the resulting problem is rather complex and often requires some computational effort. Thus, for quasi-interpolants defined from a piecewise polynomial function, φ, we propose a simpler minimization problem, based on the Bernstein–Bézier representation of some related piecewise polynomial functions, leading to a new class of quasi-interpolants.

Suggested Citation

  • Abbadi, A. & Ibáñez, M.J. & Sbibih, D., 2011. "Computing quasi-interpolants from the B-form of B-splines," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(10), pages 1936-1948.
    • Handle: RePEc:eee:matcom:v:81:y:2011:i:10:p:1936-1948
    DOI: 10.1016/j.matcom.2010.12.005
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    References listed on IDEAS

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    1. Fortes, M.A. & Ibáñez, M.J. & Rodríguez, M.L., 2009. "On Chebyshev-type integral quasi-interpolation operators," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(12), pages 3478-3491.
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    Cited by:

    1. Boujraf, A. & Tahrichi, M. & Tijini, A., 2015. "C1 Superconvergent quasi-interpolation based on polar forms," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 118(C), pages 102-115.
    2. Sbibih, D. & Serghini, A. & Tijini, A., 2015. "Superconvergent local quasi-interpolants based on special multivariate quadratic spline space over a refined quadrangulation," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 145-156.
    3. Allouch, C. & Boujraf, A. & Tahrichi, M., 2017. "Superconvergent spline quasi-interpolants and an application to numerical integration," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 137(C), pages 90-108.

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    1. Sbibih, D. & Serghini, A. & Tijini, A., 2015. "Superconvergent local quasi-interpolants based on special multivariate quadratic spline space over a refined quadrangulation," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 145-156.
    2. Allouch, C. & Boujraf, A. & Tahrichi, M., 2017. "Superconvergent spline quasi-interpolants and an application to numerical integration," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 137(C), pages 90-108.
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