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Central orderings for the Newton interpolation formula

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Abstract

The stability properties of the Newton interpolation formula depend on the order of the nodes and can be measured through a condition number. Increasing and Leja orderings have been previously considered (Carnicer et al. in J Approx Theory, 2017. https://doi.org/10.1016/j.jat.2017.07.005; Reichel in BIT 30:332–346, 1990). We analyze central orderings for equidistant nodes on a bounded real interval. A bound for conditioning is given. We demonstrate in particular that this ordering provides a more stable Newton formula than the natural increasing order. We also analyze of a central ordering with respect to the evaluation point, which provides low bounds for the conditioning. Numerical examples are included.

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Acknowledgements

This work has been partially supported by the Spanish Research Grant MTM2015-65433-P (MINECO/FEDER), BES-2013-065398B (MINECO), by Gobierno the Aragón and Fondo Social Europeo.

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  1. Departamento de Matemática Aplicada/IUMA, Universidad de Zaragoza, Zaragoza, Spain

    J. M. Carnicer, Y. Khiar & J. M. Peña

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  1. J. M. Carnicer
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  2. Y. Khiar
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  3. J. M. Peña
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Correspondence to Y. Khiar.

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Communicated by Michael S. Floater.

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Carnicer, J.M., Khiar, Y. & Peña, J.M. Central orderings for the Newton interpolation formula. Bit Numer Math 59, 371–386 (2019). https://doi.org/10.1007/s10543-018-00743-2

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  • DOI: https://doi.org/10.1007/s10543-018-00743-2

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