Using a Chebyshev Polynomial of the First Kind , define

Then

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.

© 1996-9

1999-05-26