BIT Numerical Mathematics | 2019

Central orderings for the Newton interpolation formula



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.; 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.

Volume None
Pages 1-16
DOI 10.1007/S10543-018-00743-2
Language English
Journal BIT Numerical Mathematics

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