Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Matrix computations (3rd ed.)
Barycentric rational interpolation with no poles and high rates of approximation
Numerische Mathematik
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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.