Inverse central ordering for the Newton interpolation formula

Inverse central ordering for the Newton interpolation formula

An inverse central ordering of the nodes is proposed for the Newton interpolation formula. This ordering may improve the stability for certain distributions of nodes. For equidistant nodes, an upper bound of the conditioning is provided. This bound is close to the bound of the conditioning in the La...

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Veröffentlicht in:Numerical algorithms 2022-08, Vol.90 (4), p.1691-1713
Hauptverfasser: Carnicer, J. M., Khiar, Y., Peña, J. M.
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Algorithms
Codes
Computer Science
Conditioning
Hypotheses
Interpolation
Nodes
Numeric Computing
Numerical Analysis
Original Paper
Theory of Computation
Upper bounds
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Khiar, Y.
Peña, J. M.
description An inverse central ordering of the nodes is proposed for the Newton interpolation formula. This ordering may improve the stability for certain distributions of nodes. For equidistant nodes, an upper bound of the conditioning is provided. This bound is close to the bound of the conditioning in the Lagrange interpolation formula, whose conditioning is the lowest. This ordering is related to a pivoting strategy of a matrix elimination procedure called Neville elimination. The results are illustrated with examples.
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subjects Algebra
Algorithms
Codes
Computer Science
Conditioning
Hypotheses
Interpolation
Nodes
Numeric Computing
Numerical Analysis
Original Paper
Theory of Computation
Upper bounds
title Inverse central ordering for the Newton interpolation formula
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