A Mapped Polynomial Method for High-Accuracy Approximations on Arbitrary Grids

  title={A Mapped Polynomial Method for High-Accuracy Approximations on Arbitrary Grids},
  author={Ben Adcock and Rodrigo B. Platte},
  journal={SIAM J. Numer. Anal.},
  • B. Adcock, R. Platte
  • Published 19 July 2016
  • Mathematics, Computer Science
  • SIAM J. Numer. Anal.
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… 
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