math-functions-0.1.6.0: Special functions and Chebyshev polynomials

Copyright (c) 2009 2011 Bryan O'Sullivan BSD3 bos@serpentine.com experimental portable None Haskell98

Numeric.Polynomial.Chebyshev

Contents

Description

Chebyshev polynomials.

Synopsis

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

Arguments

 :: 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.

Arguments

 :: 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.