A Mapped Polynomial Method for High-Accuracy Approximations on Arbitrary Grids
Abstract
The focus of this paper is the approximation of analytic functions on compact intervals from their pointwise values on arbitrary grids. We introduce a new method for this problem based on mapped polynomial approximation. By careful selection of the mapping parameter, we ensure both high accuracy of the approximation and an asymptotically optimal scaling of the polynomial degree with the grid spacing. As we explain, efficient implementation of this method can be achieved using nonuniform fast Fourier transforms. Numerical results demonstrate the efficiency and accuracy of this approach.
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© 2016, Society for Industrial and Applied Mathematics.
History
Submitted: 1 June 2015
Accepted: 2 May 2016
Published online: 19 July 2016
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Funding Information
Alfred P. Sloan Foundationhttp://dx.doi.org/10.13039/100000879
Air Force Office of Scientific Researchhttp://dx.doi.org/10.13039/100000181: FA9550-15-1-015
National Science Foundationhttp://dx.doi.org/10.13039/100000001: DMS1522639
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