Lower bounds for the approximation with variation-diminishing splines

J. Nagler; P. Cerejeiras; B. Forster

doi:10.1016/j.jco.2015.08.002

Lower bounds for the approximation with variation-diminishing splines

J. Nagler, P. Cerejeiras, B. Forster

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We prove lower bounds for the approximation error of the variation-diminishing Schoenberg operator on the interval [0,1] in terms of classical moduli of smoothness depending on the degree of the spline basis. For this purpose we use a functional analysis framework in order to characterize the spectrum of the Schoenberg operator and investigate the asymptotic behavior of its iterates.

Original language	English
Pages (from-to)	81-91
Number of pages	11
Journal	Journal of Complexity
Volume	32
Issue number	1
DOIs	https://doi.org/10.1016/j.jco.2015.08.002
State	Published - 1 Feb 2016
Externally published	Yes

Keywords

Inverse theorem
Iterates
Schoenberg operator
Spectral theory

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10.1016/j.jco.2015.08.002

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abstract = "We prove lower bounds for the approximation error of the variation-diminishing Schoenberg operator on the interval [0,1] in terms of classical moduli of smoothness depending on the degree of the spline basis. For this purpose we use a functional analysis framework in order to characterize the spectrum of the Schoenberg operator and investigate the asymptotic behavior of its iterates.",

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AU - Cerejeiras, P.

AU - Forster, B.

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N2 - We prove lower bounds for the approximation error of the variation-diminishing Schoenberg operator on the interval [0,1] in terms of classical moduli of smoothness depending on the degree of the spline basis. For this purpose we use a functional analysis framework in order to characterize the spectrum of the Schoenberg operator and investigate the asymptotic behavior of its iterates.

AB - We prove lower bounds for the approximation error of the variation-diminishing Schoenberg operator on the interval [0,1] in terms of classical moduli of smoothness depending on the degree of the spline basis. For this purpose we use a functional analysis framework in order to characterize the spectrum of the Schoenberg operator and investigate the asymptotic behavior of its iterates.

KW - Inverse theorem

KW - Iterates

KW - Schoenberg operator

KW - Spectral theory

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JO - Journal of Complexity

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Lower bounds for the approximation with variation-diminishing splines

Abstract

Keywords

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