Devon McCormick wrote: > I might point out that the version I submitted provides the framework for > a > general inverse of a cdf, unlike the undoubtedly superior, but very > arbitrary-coefficienty version, to which John refers. >
I take Devon's point about generality and arbitrariness. What is not apparent in the page I cited is that there is a general method lying behind it, but the page joins it in progress. Chebyshev polynomials tend to get used to approximate functions over a range (Lagrange polynomials are exact at some points, but may be way off in between). In this case rational functions made from Chebyshev polynomials are used. There is a way (the Remes or Remez algorithm) for getting optimal coefficients given some conditions, and these are the magic numbers presented. If you refer to W. J. Cody, Rational Chebyshev approximations for the error function, Math. Comp., pp. 631-638, 1969. you will find calculations accurate to 3e_20 done on a CDC 3600. Given that the xth Chebyshev polynomial evaluated at y can be written cos x*arccos y is there a way to write it using inverses? Best wishes, John ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
