Numeric.Polynomial.Chebyshev
Contents
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, and so
gives different results than chebyshev for the same inputs.
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.