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Lagrange interpolation on extended generalized Jacobi nodes

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Abstract

We consider theL p-convergence of interpolatory processes for nonsmooth functions. Therefore we use generalizations of the well-known Marcinkiewicz-Zygmund inequality for trigonometric polynomials to the case of algebraic polynomials, extending a result of Y. Xu. Particularly, we obtain the order of convergence for certain Lagrange and quasi-Lagrange interpolatory processes on generalized Jacobi nodes. Our approach enables us also to discuss the influence of additional nodes near the endpoints ±1.

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Authors and Affiliations

  1. Fachbereich Mathematik, UniversitÄt Rostock, D-18051, Rostock, Germany

    Jürgen Prestin

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  1. Jürgen Prestin
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Prestin, J. Lagrange interpolation on extended generalized Jacobi nodes. Numer Algor 5, 179–190 (1993). https://doi.org/10.1007/BF02215680

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  • DOI: https://doi.org/10.1007/BF02215680

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