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Open AccessArticle

Classical Lagrange Interpolation Based on General Nodal Systems at Perturbed Roots of Unity

1
Departamento de Matemática Aplicada I, Universidad de Vigo, 36201 Vigo, Pontevedra, Spain
2
Departamento de Matemáticas, Instituto E. S. Valle Inclán, 36001 Pontevedra, Spain
*
Authors to whom correspondence should be addressed.
These authors contributed equally to this work.
Mathematics 2020, 8(4), 498; https://doi.org/10.3390/math8040498
Received: 28 February 2020 / Revised: 25 March 2020 / Accepted: 29 March 2020 / Published: 2 April 2020
(This article belongs to the Special Issue Functional Statistics: Outliers Detection and Quality Control)
The aim of this paper is to study the Lagrange interpolation on the unit circle taking only into account the separation properties of the nodal points. The novelty of this paper is that we do not consider nodal systems connected with orthogonal or paraorthogonal polynomials, which is an interesting approach because in practical applications this connection may not exist. A detailed study of the properties satisfied by the nodal system and the corresponding nodal polynomial is presented. We obtain the relevant results of the convergence related to the process for continuous smooth functions as well as the rate of convergence. Analogous results for interpolation on the bounded interval are deduced and finally some numerical examples are presented. View Full-Text
Keywords: Lagrange interpolation; unit circle; nodal systems; separation properties; perturbed roots of the unity; convergence Lagrange interpolation; unit circle; nodal systems; separation properties; perturbed roots of the unity; convergence
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MDPI and ACS Style

Berriochoa, E.; Cachafeiro, A.; Castejón, A.; García-Amor, J.M. Classical Lagrange Interpolation Based on General Nodal Systems at Perturbed Roots of Unity. Mathematics 2020, 8, 498.

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