Recursive polynomial interpolation algorithm (RPIA)
type: Item
instance of: scholarly article
title: Recursive polynomial interpolation algorithm (RPIA)
zbMATH Open document ID: 1386.65070
author: A. Messaoudi
author: Hassane Sadok
published in: Numerical Algorithms
publication date: 2017-11-24T00:00:00Z
review text: The paper under review is focused on the polynomial interpolation problem, i.e. on the computation of a planar interpolation polynomial of \(n\)-th degree passing through a set of \(n+1\) points with no two \(x\)-coordinates equal. A new method -- recursive polynomial interpolation algorithm (RPIA) -- for interpolation polynomial computation is described. RPIA consists in a reformulation of the polynomial interpolation problem and the expression of interpolation polynomials as Schur complements. For the construction of RPIA, the properties of the Schur complements and the Sylvester identity are applied. Lagrange and Newton formulas commonly used to obtain interpolation polynomials are mentioned in the paper, too. The explanation of RPIA construction is completed by several examples where the new algorithm is applied. The suggested method can be applied in various areas of numerical analysis, digital signal processing, computer graphics, etc.
reviewed by: Ivana Linkeová
Mathematics Subject Classification ID: 65D05
zbMATH DE Number: 6812485
zbMATH Keywords: polynomial interpolation
zbMATH Keywords: Lagrange method
zbMATH Keywords: Newton method
zbMATH Keywords: Vandermonde matrix
zbMATH Keywords: Schur complement
zbMATH Keywords: Sylvester identity
zbMATH Keywords: recursive interpolation algorithm
zbMATH Keywords: recursive polynomial interpolation algorithm
describes a project that uses: OPQ
MaRDI profile type: Publication
full work available at URL: s11075-017-0276-2
OpenAlex ID: W2588664555
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DOI: 10.1007/S11075-017-0276-2
description: scientific article; zbMATH DE number 6812485