Local RBF approximation for scattered data fitting with bivariate splines

O. Davydov, A. Sestini, R. Morandi

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

In this paper we continue our earlier research [4] aimed at developing effcient methods of local approximation suitable for the first stage of a spline based two-stage scattered data fitting algorithm. As an improvement to the pure polynomial local approximation method used in [5], a hybrid polynomial/radial basis scheme was considered in [4], where the local knot locations for the RBF terms were selected using a greedy knot insertion algorithm. In this paper standard radial local approximations based on interpolation or least squares are considered and a faster procedure is used for knot selection, signicantly reducing the computational cost of the method. Error analysis of the method and numerical results illustrating its performance are given.
LanguageEnglish
Title of host publicationTrends and Applications in Constructive Approximation
EditorsDetlef H. Mache, József Szabados, Marcel G. de Bruin
Place of PublicationBerlin, Germany
Pages91-102
Number of pages11
Volume151
DOIs
Publication statusPublished - 2005

Publication series

NameInternational Series of Numerical Mathematics
PublisherBirkhäuser (Springer)

Fingerprint

Splines
Polynomials
Error analysis
Interpolation
Costs

Keywords

  • scattered data fitting
  • bivariate splines
  • constructive approximation

Cite this

Davydov, O., Sestini, A., & Morandi, R. (2005). Local RBF approximation for scattered data fitting with bivariate splines. In D. H. Mache, J. Szabados, & M. G. de Bruin (Eds.), Trends and Applications in Constructive Approximation (Vol. 151, pp. 91-102). (International Series of Numerical Mathematics). Berlin, Germany. https://doi.org/10.1007/3-7643-7356-3_8
Davydov, O. ; Sestini, A. ; Morandi, R. / Local RBF approximation for scattered data fitting with bivariate splines. Trends and Applications in Constructive Approximation. editor / Detlef H. Mache ; József Szabados ; Marcel G. de Bruin. Vol. 151 Berlin, Germany, 2005. pp. 91-102 (International Series of Numerical Mathematics).
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Davydov, O, Sestini, A & Morandi, R 2005, Local RBF approximation for scattered data fitting with bivariate splines. in DH Mache, J Szabados & MG de Bruin (eds), Trends and Applications in Constructive Approximation. vol. 151, International Series of Numerical Mathematics, Berlin, Germany, pp. 91-102. https://doi.org/10.1007/3-7643-7356-3_8

Local RBF approximation for scattered data fitting with bivariate splines. / Davydov, O.; Sestini, A.; Morandi, R.

Trends and Applications in Constructive Approximation. ed. / Detlef H. Mache; József Szabados; Marcel G. de Bruin. Vol. 151 Berlin, Germany, 2005. p. 91-102 (International Series of Numerical Mathematics).

Research output: Chapter in Book/Report/Conference proceedingChapter

TY - CHAP

T1 - Local RBF approximation for scattered data fitting with bivariate splines

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AU - Sestini, A.

AU - Morandi, R.

PY - 2005

Y1 - 2005

N2 - In this paper we continue our earlier research [4] aimed at developing effcient methods of local approximation suitable for the first stage of a spline based two-stage scattered data fitting algorithm. As an improvement to the pure polynomial local approximation method used in [5], a hybrid polynomial/radial basis scheme was considered in [4], where the local knot locations for the RBF terms were selected using a greedy knot insertion algorithm. In this paper standard radial local approximations based on interpolation or least squares are considered and a faster procedure is used for knot selection, signicantly reducing the computational cost of the method. Error analysis of the method and numerical results illustrating its performance are given.

AB - In this paper we continue our earlier research [4] aimed at developing effcient methods of local approximation suitable for the first stage of a spline based two-stage scattered data fitting algorithm. As an improvement to the pure polynomial local approximation method used in [5], a hybrid polynomial/radial basis scheme was considered in [4], where the local knot locations for the RBF terms were selected using a greedy knot insertion algorithm. In this paper standard radial local approximations based on interpolation or least squares are considered and a faster procedure is used for knot selection, signicantly reducing the computational cost of the method. Error analysis of the method and numerical results illustrating its performance are given.

KW - scattered data fitting

KW - bivariate splines

KW - constructive approximation

U2 - 10.1007/3-7643-7356-3_8

DO - 10.1007/3-7643-7356-3_8

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SN - 3764371242

VL - 151

T3 - International Series of Numerical Mathematics

SP - 91

EP - 102

BT - Trends and Applications in Constructive Approximation

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A2 - Szabados, József

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ER -

Davydov O, Sestini A, Morandi R. Local RBF approximation for scattered data fitting with bivariate splines. In Mache DH, Szabados J, de Bruin MG, editors, Trends and Applications in Constructive Approximation. Vol. 151. Berlin, Germany. 2005. p. 91-102. (International Series of Numerical Mathematics). https://doi.org/10.1007/3-7643-7356-3_8