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 xi argument (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.