Central orderings for the Newton interpolation formula
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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.
KeywordsNewton interpolation formula Conditioning Central ordering
Mathematics Subject Classification65D05 65F35 41A05 41A10
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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