On weighted average interpolation with cardinal splines

López-Salazar Codes, Jeronimo and Pérez Villalón, Gerardo (2017). On weighted average interpolation with cardinal splines. "Acta Applicandae Mathematicae", v. 152 (n. 1); pp. 73-82. ISSN 0167-8019. https://doi.org/10.1007/s10440-017-0112-7.

Description

Title: On weighted average interpolation with cardinal splines
Author/s:
  • López-Salazar Codes, Jeronimo
  • Pérez Villalón, Gerardo
Item Type: Article
Título de Revista/Publicación: Acta Applicandae Mathematicae
Date: 28 July 2017
ISSN: 0167-8019
Volume: 152
Subjects:
Freetext Keywords: Spline; cardinal interpolation; average sampling
Faculty: E.T.S.I. y Sistemas de Telecomunicación (UPM)
Department: Matemática Aplicada a las Tecnologías de la Información y las Comunicaciones
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

Given a sequence of data {yn}n∈Z with polynomial growth and an odd number d, Schoenberg proved that there exists a unique cardinal spline f of degree d with polynomial growth such that f (n) = yn for all n ∈ Z. In this work, we show that this result also holds if we consider weighted average data f ∗ h(n) = yn, whenever the average function h satisfies some light conditions. In particular, the interpolation result is valid if we consider cellaverage data n+a n−a f (x)dx = yn with 0 < a ≤ 1/2. The case of even degree d is also studied.

More information

Item ID: 53473
DC Identifier: http://oa.upm.es/53473/
OAI Identifier: oai:oa.upm.es:53473
DOI: 10.1007/s10440-017-0112-7
Official URL: https://link.springer.com/article/10.1007/s10440-017-0112-7
Deposited by: Memoria Investigacion
Deposited on: 31 Jan 2019 15:03
Last Modified: 31 Jan 2019 15:03
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