Numeric.Polynomial.Chebyshev

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

chebyshev

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.

chebyshevBroucke

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.