The Discrete k-Functional and Spline Smoothing of Noisy Data

Estimation of a function f from a finite sample y = [ f(xi) + εi], xi∈ [ a, b ], subject to random noise εi, is a basic problem of numerical approximation theory. This paper defines a discrete analog, km(y, λ), of Peetre's K-functional, which relates to spline smoothing. We show how to use kman...

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Bibliographic Details
Published in:SIAM journal on numerical analysis 1985-12, Vol.22 (6), p.1243-1254
Main Author: Ragozin, David L.
Format: Article
Language:English
Subjects:
Approximation
Data smoothing
Eigenvalues
Exact sciences and technology
Fourier transformations
Information retrieval noise
Inner products
Mathematical functions
Mathematical inequalities
Mathematical vectors
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical approximation
Sciences and techniques of general use
Slope of a line
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Summary:Estimation of a function f from a finite sample y = [ f(xi) + εi], xi∈ [ a, b ], subject to random noise εi, is a basic problem of numerical approximation theory. This paper defines a discrete analog, km(y, λ), of Peetre's K-functional, which relates to spline smoothing. We show how to use kmand its connection to the mth order modulus of continuity to assess the smoothness of f and to choose a good smoothing spline approximation to f and some of its derivatives.
ISSN:0036-1429
1095-7170
DOI:10.1137/0722077