minimaxApprox
Minimax Approximation of Functions by Polynomials and Rational Functions
Implements minimax approximation of functions via the Remez
(1962) algorithm for polynomials and the Cody-Fraser-Hart (1968)
title: Package minimaxApprox
Description
minimaxApprox is an R package which implements minimax approximation of
functions via the Remez (1962) algorithm for polynomials and the
Cody-Fraser-Hart (1968) doi:10.1007/BF02162506 algorithm for rational
functions, as well as their barycentric formulations: the Pachón-Trefethen
(2009) doi:10.1007/s10543-009-0240-1 algorithm for polynomials and the
Filip-Nakatsukasa-Trefethen-Beckermann (2018) doi:10.1137/17M1132409 algorithm
for rational functions, which provide improved numerical stability at higher
degrees and on wider intervals.
Citation
If you use the package, please cite it as per CITATION.
Acknowledgments
The author is grateful to Martin Maechler for suggestions which helped the author's introduction to minimax approximation.
Roadmap
Major
- Remove the
xiargument (deprecated in 0.6.0): the redesigned exchange derives its reference from the error curve directly, making a user-supplied initial reference unnecessary. - Exploit even/odd symmetry via the t = x² substitution: half-degree solves with structurally exact zero coefficients for functions of known parity on symmetric intervals.
- Report the dense-grid supremum on non-converged exits, so that warned results carry an honest error bound rather than the final reference's leveled error.
Minor
- Make the near-machine-precision warning threshold magnitude-relative rather than absolute.
- Validate that the function evaluates finitely on the interval, with a clear message rather than a downstream error.
- Assorted message formatting (e.g. the NaN convergence-ratio text when the observed error is exactly zero).
Contributions
Please see CONTRIBUTING.md.
Security
Please see SECURITY.md.