A particular smooth interpolation that generates splines

Segeth, Karel

  • Programs and Algorithms of Numerical Mathematics, Publisher: Institute of Mathematics CAS(Prague), page 112-119

Abstract

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There are two grounds the spline theory stems from - the algebraic one (where splines are understood as piecewise smooth functions satisfying some continuity conditions) and the variational one (where splines are obtained via minimization of some quadratic functionals with constraints). We use the general variational approach called smooth interpolation introduced by Talmi and Gilat and show that it covers not only the cubic spline and its 2D and 3D analogues but also the well known tension spline (called also spline with tension). We present the results of a 1D numerical example that characterize some properties of the tension spline.

How to cite

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Segeth, Karel. "A particular smooth interpolation that generates splines." Programs and Algorithms of Numerical Mathematics. Prague: Institute of Mathematics CAS, 2017. 112-119. <http://eudml.org/doc/288169>.

@inProceedings{Segeth2017,
abstract = {There are two grounds the spline theory stems from - the algebraic one (where splines are understood as piecewise smooth functions satisfying some continuity conditions) and the variational one (where splines are obtained via minimization of some quadratic functionals with constraints). We use the general variational approach called smooth interpolation introduced by Talmi and Gilat and show that it covers not only the cubic spline and its 2D and 3D analogues but also the well known tension spline (called also spline with tension). We present the results of a 1D numerical example that characterize some properties of the tension spline.},
author = {Segeth, Karel},
booktitle = {Programs and Algorithms of Numerical Mathematics},
keywords = {data interpolation; smooth interpolation; spline interpolation; tension spline; Fourier series; Fourier transform},
location = {Prague},
pages = {112-119},
publisher = {Institute of Mathematics CAS},
title = {A particular smooth interpolation that generates splines},
url = {http://eudml.org/doc/288169},
year = {2017},
}

TY - CLSWK
AU - Segeth, Karel
TI - A particular smooth interpolation that generates splines
T2 - Programs and Algorithms of Numerical Mathematics
PY - 2017
CY - Prague
PB - Institute of Mathematics CAS
SP - 112
EP - 119
AB - There are two grounds the spline theory stems from - the algebraic one (where splines are understood as piecewise smooth functions satisfying some continuity conditions) and the variational one (where splines are obtained via minimization of some quadratic functionals with constraints). We use the general variational approach called smooth interpolation introduced by Talmi and Gilat and show that it covers not only the cubic spline and its 2D and 3D analogues but also the well known tension spline (called also spline with tension). We present the results of a 1D numerical example that characterize some properties of the tension spline.
KW - data interpolation; smooth interpolation; spline interpolation; tension spline; Fourier series; Fourier transform
UR - http://eudml.org/doc/288169
ER -

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