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On Chebyshev-type integral quasi-interpolation operators

Author

Listed:
  • Fortes, M.A.
  • Ibáñez, M.J.
  • Rodríguez, M.L.

Abstract

Spline quasi-interpolants on the real line are approximating splines to given functions with optimal approximation orders. They are called integral quasi-interpolants if the coefficients in the spline series are linear combinations of weighted mean values of the function to be approximated. This paper is devoted to the construction of new integral quasi-interpolants with compactly supported piecewise polynomial weights. The basic idea consists of minimizing an expression appearing in an estimate for the quasi-interpolation error. It depends on how well the quasi-interpolation operator approximates the first non-reproduced monomial. Explicit solutions as well as some numerical tests in the B-spline case are given.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:79:y:2009:i:12:p:3478-3491
    DOI: 10.1016/j.matcom.2009.04.014
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    Cited by:

    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.
    3. Gao, Wenwu & Zhang, Xia & Zhou, Xuan, 2020. "Multiquadric quasi-interpolation for integral functionals," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 177(C), pages 316-328.
    4. 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.

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