Faster fast evaluation of thin plate splines in two dimensions

A new method for fast evaluation of thin plate splines in two dimensions is presented. The paper first develops exponential approximations to thin plate splines. These are the analytical basis for an improved fast multipole evaluator. Analytic error bounds are supplemented by offline parallel numeri...

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Veröffentlicht in:Journal of computational and applied mathematics Jg. 261; S. 201 - 212
Hauptverfasser: Beatson, R.K., Ong, W.E., Rychkov, I.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 01.05.2014
Schlagworte:
Exponential approximation
Fast evaluation
Thin plate splines
65C20
41A58
41A30
Fast evaluation
65D10
Thin plate splines
Exponential approximation
ISSN:0377-0427, 1879-1778
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Abstract A new method for fast evaluation of thin plate splines in two dimensions is presented. The paper first develops exponential approximations to thin plate splines. These are the analytical basis for an improved fast multipole evaluator. Analytic error bounds are supplemented by offline parallel numerical computation of the underlying error constants. These error constants enable adaptive selection of series lengths as a function of the weights associated with a source panel, and the desired accuracy. Numerical comparisons with a competing algorithm show that the new method is significantly faster when moderate to high precision is required.
AbstractList A new method for fast evaluation of thin plate splines in two dimensions is presented. The paper first develops exponential approximations to thin plate splines. These are the analytical basis for an improved fast multipole evaluator. Analytic error bounds are supplemented by offline parallel numerical computation of the underlying error constants. These error constants enable adaptive selection of series lengths as a function of the weights associated with a source panel, and the desired accuracy. Numerical comparisons with a competing algorithm show that the new method is significantly faster when moderate to high precision is required.
Author Ong, W.E.
Beatson, R.K.
Rychkov, I.
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crossref_primary_10_1016_j_applthermaleng_2017_06_071
Cites_doi 10.1016/0898-1221(92)90167-G
10.1137/S1064827596310779
10.1137/S106482759630989X
10.1137/S1064827502400984
10.1007/s00211-004-0538-5
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Keywords 65C20
41A58
41A30
Fast evaluation
65D10
Thin plate splines
Exponential approximation
Language English
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References D. Potts, et al. Fast summation based on NFFT.
Yarvin, Rokhlin (br000040) 1998; 20
Wendland (br000010) 2005
1996.
Beatson, Newsam (br000005) 1992; 24
Potts, Steidl (br000020) 2003; 24
Hrycak, Rokhlin (br000015) 1998; 19
Boas (br000050) 1954
Potts, Steidl, Nieslony (br000025) 2004; 98
2006.
N. Yarvin, V. Rokhlin, Generalized Gaussian quadratures.
Beatson, Greengard (br000035) 1997
Hrycak (10.1016/j.cam.2013.11.005_br000015) 1998; 19
Beatson (10.1016/j.cam.2013.11.005_br000005) 1992; 24
10.1016/j.cam.2013.11.005_br000045
Boas (10.1016/j.cam.2013.11.005_br000050) 1954
Yarvin (10.1016/j.cam.2013.11.005_br000040) 1998; 20
Wendland (10.1016/j.cam.2013.11.005_br000010) 2005
10.1016/j.cam.2013.11.005_br000030
Potts (10.1016/j.cam.2013.11.005_br000025) 2004; 98
Potts (10.1016/j.cam.2013.11.005_br000020) 2003; 24
Beatson (10.1016/j.cam.2013.11.005_br000035) 1997
References_xml – volume: 19
  start-page: 1804
  year: 1998
  end-page: 1826
  ident: br000015
  article-title: An improved fast multipole algorithm for potential fields
  publication-title: SIAM J. Sci. Comput.
– year: 2005
  ident: br000010
  article-title: Scattered Data Approximation
– reference: , 2006.
– start-page: 1
  year: 1997
  end-page: 37
  ident: br000035
  article-title: A short course on fast multiple methods
  publication-title: Multilevel Methods Elliptic PDEs Wavelets
– volume: 24
  start-page: 2013
  year: 2003
  end-page: 2037
  ident: br000020
  article-title: Fast summation at nonequispaced knots by NFFT
  publication-title: SIAM J. Sci. Comput.
– volume: 24
  start-page: 7
  year: 1992
  end-page: 19
  ident: br000005
  article-title: Fast evaluation of radial basis functions, I
  publication-title: Comput. Math. Appl.
– volume: 98
  start-page: 329
  year: 2004
  end-page: 351
  ident: br000025
  article-title: Fast convolution with radial kernels at nonequispaced knots
  publication-title: Numer. Math.
– volume: 20
  start-page: 699
  year: 1998
  end-page: 718
  ident: br000040
  article-title: Generalized Gaussian quadratures and singular value decomposition of integral operators
  publication-title: SIAM J. Sci. Comput.
– reference: D. Potts, et al. Fast summation based on NFFT.
– reference: N. Yarvin, V. Rokhlin, Generalized Gaussian quadratures.
– year: 1954
  ident: br000050
  article-title: Entire Functions
– reference: , 1996.
– volume: 24
  start-page: 7
  year: 1992
  ident: 10.1016/j.cam.2013.11.005_br000005
  article-title: Fast evaluation of radial basis functions, I
  publication-title: Comput. Math. Appl.
  doi: 10.1016/0898-1221(92)90167-G
– year: 1954
  ident: 10.1016/j.cam.2013.11.005_br000050
– volume: 20
  start-page: 699
  year: 1998
  ident: 10.1016/j.cam.2013.11.005_br000040
  article-title: Generalized Gaussian quadratures and singular value decomposition of integral operators
  publication-title: SIAM J. Sci. Comput.
  doi: 10.1137/S1064827596310779
– ident: 10.1016/j.cam.2013.11.005_br000045
– volume: 19
  start-page: 1804
  year: 1998
  ident: 10.1016/j.cam.2013.11.005_br000015
  article-title: An improved fast multipole algorithm for potential fields
  publication-title: SIAM J. Sci. Comput.
  doi: 10.1137/S106482759630989X
– volume: 24
  start-page: 2013
  issue: 6
  year: 2003
  ident: 10.1016/j.cam.2013.11.005_br000020
  article-title: Fast summation at nonequispaced knots by NFFT
  publication-title: SIAM J. Sci. Comput.
  doi: 10.1137/S1064827502400984
– ident: 10.1016/j.cam.2013.11.005_br000030
– volume: 98
  start-page: 329
  year: 2004
  ident: 10.1016/j.cam.2013.11.005_br000025
  article-title: Fast convolution with radial kernels at nonequispaced knots
  publication-title: Numer. Math.
  doi: 10.1007/s00211-004-0538-5
– year: 2005
  ident: 10.1016/j.cam.2013.11.005_br000010
– start-page: 1
  year: 1997
  ident: 10.1016/j.cam.2013.11.005_br000035
  article-title: A short course on fast multiple methods
  publication-title: Multilevel Methods Elliptic PDEs Wavelets
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SubjectTerms Exponential approximation
Fast evaluation
Thin plate splines
Title Faster fast evaluation of thin plate splines in two dimensions
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