EfficientL 2 approximation by splines

descriptionPublicationkeyboard_double_arrow_right Article 01 Mar 1979 Germany English Publisher:Springer Science and Business Media LLCJournal:Numerische Mathematik, volume 33, pages 101-114 (issn: 0029-599X, eissn: 0945-3245,

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Authors: Barrow, D.L.; Smith, P.W.;

doi: 10.1007/bf01396498

EfficientL 2 approximation by splines

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Abstract

LetS N k (t) be the linear space ofk-th order splines on [0, 1] having the simple knotst i determined from a fixed functiont by the rulet i=t(i/N). In this paper we introduce sequences of operators {Q N } N ? =1 fromC k [0, 1] toS N k (t) which are computationally simple and which, asN??, give essentially the best possible approximations tof and its firstk?1 derivatives, in the norm ofL 2[0, 1]. Precisely, we show thatN k?1(?(f?Q N f) i ??dist2(f (1),S N k?1 (t)))?0 fori=0, 1, ...,k?1. Several numerical examples are given.

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Germany

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The University of Texas System
United States
Texas A&M University
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DigiZeitschriften
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Keywords

Best approximation, Chebyshev systems, 510.mathematics, Spline approximation, splines, L2 approximation, Article, Numerical computation using splines

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