Portability | portable |
---|---|

Stability | experimental |

Maintainer | bos@serpentine.com |

Safe Haskell | None |

Chebyshev polynomials.

# Chebyshev polinomials

A Chebyshev polynomial of the first kind is defined by the following recurrence:

t 0 _ = 1 t 1 x = x t n x = 2 * x * t (n-1) x - t (n-2) x

:: Vector v Double | |

=> Double | Parameter of each function. |

-> v Double | Coefficients of each polynomial term, in increasing order. |

-> Double |

Evaluate a Chebyshev polynomial of the first kind. Uses Clenshaw's algorithm.

:: Vector v Double | |

=> Double | Parameter of each function. |

-> v Double | Coefficients of each polynomial term, in increasing order. |

-> Double |

Evaluate a Chebyshev polynomial of the first kind. Uses Broucke's ECHEB algorithm, and his convention for coefficient handling. It treat 0th coefficient different so

chebyshev x [a0,a1,a2...] == chebyshevBroucke [2*a0,a1,a2...]

# References

- Broucke, R. (1973) Algorithm 446: Ten subroutines for the
manipulation of Chebyshev series.
*Communications of the ACM*16(4):254–256. http://doi.acm.org/10.1145/362003.362037 - Clenshaw, C.W. (1962) Chebyshev series for mathematical
functions.
*National Physical Laboratory Mathematical Tables 5*, Her Majesty's Stationery Office, London.