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Recent Progress on Univariate and Multivariate Polynomial and Spline Quasi-interpolants

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Trends and Applications in Constructive Approximation

Part of the book series: ISNM International Series of Numerical Mathematics ((ISNM,volume 151))

Abstract

Polynomial and spline quasi-interpolants (QIs) are practical and effective approximation operators. Among their remarkable properties, let us cite for example: good shape properties, easy computation and evaluation (no linear system to solve), uniform boundedness independently of the degree (polynomials) or of the partition (splines), good approximation order. We shall emphasize new results on various types of univariate and multivariate polynomial or spline QIs, depending on the nature of coefficient functionals, which can be differential, discrete or integral We shall also present some applications of QIs to numerical methods.

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Authors and Affiliations

  1. Centre de Mathématiques, INSA de Rennes, 20 Avenue des Buttes de Coësmes, CS 14315, F-35043, Rennes cedex, France

    Paul Sablonnière

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  1. Paul Sablonnière
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Editors and Affiliations

  1. FB3, Applied Mathematics (Constructive Approximation), University of Applied Science Bochum, Herner Str. 45, D-44787, Bochum

    Detlef H. Mache

  2. Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, P.O. Box 127, H-1364, Budapest

    József Szabados

  3. Department of Applied Mathematics, Delft University of Technology, P.O. Box 5031, 2600 GA, Delft, The Netherlands

    Marcel G. de Bruin

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Sablonnière, P. (2005). Recent Progress on Univariate and Multivariate Polynomial and Spline Quasi-interpolants. In: Mache, D.H., Szabados, J., de Bruin, M.G. (eds) Trends and Applications in Constructive Approximation. ISNM International Series of Numerical Mathematics, vol 151. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7356-3_17

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