Spectral approach for kernel-based interpolation

Bertrand Gauthier[1]; Xavier Bay[2]

  • [1] Université Jean-Monnet de Saint-Étienne ICJ, URM 5208, PRES univ. de Lyon
  • [2] École des Mines de Saint-Étienne Institut Fayol

Annales de la faculté des sciences de Toulouse Mathématiques (2012)

  • Volume: 21, Issue: 3, page 439-479
  • ISSN: 0240-2963

Abstract

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We describe how the resolution of a kernel-based interpolation problem can be associated with a spectral problem. An integral operator is defined from the embedding of the considered Hilbert subspace into an auxiliary Hilbert space of square-integrable functions. We finally obtain a spectral representation of the interpolating elements which allows their approximation by spectral truncation. As an illustration, we show how this approach can be used to enforce boundary conditions in kernel-based interpolation models and in what it offers an interesting alternative for dimension reduction.

How to cite

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Gauthier, Bertrand, and Bay, Xavier. "Spectral approach for kernel-based interpolation." Annales de la faculté des sciences de Toulouse Mathématiques 21.3 (2012): 439-479. <http://eudml.org/doc/251022>.

@article{Gauthier2012,
abstract = {We describe how the resolution of a kernel-based interpolation problem can be associated with a spectral problem. An integral operator is defined from the embedding of the considered Hilbert subspace into an auxiliary Hilbert space of square-integrable functions. We finally obtain a spectral representation of the interpolating elements which allows their approximation by spectral truncation. As an illustration, we show how this approach can be used to enforce boundary conditions in kernel-based interpolation models and in what it offers an interesting alternative for dimension reduction.},
affiliation = {Université Jean-Monnet de Saint-Étienne ICJ, URM 5208, PRES univ. de Lyon; École des Mines de Saint-Étienne Institut Fayol},
author = {Gauthier, Bertrand, Bay, Xavier},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
language = {eng},
month = {4},
number = {3},
pages = {439-479},
publisher = {Université Paul Sabatier, Toulouse},
title = {Spectral approach for kernel-based interpolation},
url = {http://eudml.org/doc/251022},
volume = {21},
year = {2012},
}

TY - JOUR
AU - Gauthier, Bertrand
AU - Bay, Xavier
TI - Spectral approach for kernel-based interpolation
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2012/4//
PB - Université Paul Sabatier, Toulouse
VL - 21
IS - 3
SP - 439
EP - 479
AB - We describe how the resolution of a kernel-based interpolation problem can be associated with a spectral problem. An integral operator is defined from the embedding of the considered Hilbert subspace into an auxiliary Hilbert space of square-integrable functions. We finally obtain a spectral representation of the interpolating elements which allows their approximation by spectral truncation. As an illustration, we show how this approach can be used to enforce boundary conditions in kernel-based interpolation models and in what it offers an interesting alternative for dimension reduction.
LA - eng
UR - http://eudml.org/doc/251022
ER -

References

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