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The numerical stability of evaluation schemes for polynomials based on the lagrange interpolation form

  • Part II Numerical Mathematics
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Abstract

For evaluation schemes based on the Lagrangian form of a polynomial with degreen, a rigorous error analysis is performed, taking into account that data, computation and even the nodes of interpolation might be perturbed by round-off. The error norm of the scheme is betweenn 2 andn 2+(3n+7)λ n , where λ n denotes the Lebesgue constant belonging to the nodes. Hence, the error norm is of least possible orderO(n 2) if, for instance, the nodes are chosen to be the Chebyshev points or the Fekete points.

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Authors and Affiliations

  1. Lehrstuhl Mathematik III, Universität Dortmund, Postfach 500500, D-4600, Dortmund 50, BRD

    Heinz-Joachim Rack & Manfred Reimer

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  1. Heinz-Joachim Rack
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  2. Manfred Reimer
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Rack, HJ., Reimer, M. The numerical stability of evaluation schemes for polynomials based on the lagrange interpolation form. BIT 22, 101–107 (1982). https://doi.org/10.1007/BF01934399

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  • DOI: https://doi.org/10.1007/BF01934399

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