Chebyshev Approximation Formula

Using a Chebyshev polynomial of the first kind , define

			(1)
			(2)

Then

(3)

It is exact for the  zeros of . This type of approximation is important because, when truncated, the error is spread smoothly over . The Chebyshev approximation formula is very close to the minimax polynomial.

REFERENCES:

Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. "Chebyshev Approximation," "Derivatives or Integrals of a Chebyshev-Approximated Function," and "Polynomial Approximation from Chebyshev Coefficients." §5.8, 5.9, and 5.10 in Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, pp. 184-188, 189-190, and 191-192, 1992.