A Rational Interpolation Scheme with Superpolynomial Rate of Convergence

12 years 11 months ago

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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. Key words. rational interpolation, nonlinear regression, function approximation, approximation order AMS subject classifications. 41A05, 41A20, 41A25, 41A80, 62J02 DOI. 10.1137/080741574

Qiqi Wang, Parviz Moin, Gianluca Iaccarino

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