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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Bibliographic Details
Published in:Journal of computational and applied mathematics Vol. 261; pp. 201 - 212
Main Authors: Beatson, R.K., Ong, W.E., Rychkov, I.
Format: Journal Article
Language:English
Published: Elsevier B.V 01.05.2014
Subjects:
Exponential approximation
Fast evaluation
Thin plate splines
65C20
41A58
41A30
Fast evaluation
65D10
Thin plate splines
Exponential approximation
ISSN:0377-0427, 1879-1778
Online Access:Get full text
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Summary: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.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2013.11.005