A Rational Interpolation Scheme with Superpolynomial Rate of Convergence
Name
Wang-2010-A rational interpolation .pdf
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1010.62 KB
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Author(s)
Wang, Qiqi
Moin, Parviz
Iaccarino, Gianluca
Date Issued
January 2010
Journal
SIAM Journal on Numerical Analysis
Publisher
Society for Industrial and Applied Mathematics
Citation
Wang, Qiqi, Parviz Moin, and Gianluca Iaccarino. “A Rational Interpolation Scheme with Superpolynomial Rate of Convergence.” SIAM Journal on Numerical Analysis 47.6 (2010): 4073-4097. © 2010 Society for Industrial and Applied Mathematics
Version
Final published version
Abstract
The purpose of this study is to construct a high-order interpolation scheme for arbitrary scattered datasets. The resulting function approximation is an interpolation function when the dataset is exact, or a regression if measurement errors are present. We represent each datapoint with a Taylor series, and the approximation error as a combination of the derivatives of the target function. A weighted sum of the square of the coefficient of each derivative term in the approximation error is minimized to obtain the interpolation approximation. The resulting approximation function is a high-order rational function with no poles. When measurement errors are absent, the interpolation approximation converges to the target function faster than any polynomial rate of convergence.
Subjects
rational interpolation
nonlinear regression
function approximation
approximation order
MIT Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1137/080741574
