Re:Implementing Advanced Math Functions
by stephencanon on Wednesday April 25, 2012 @10:33AM
(#3889260)
It's true regardless of what your goal is (unless your goal is to play with Taylor series approximations). Even if you're going purely for speed, you can often replace a third-order Taylor series with a second-order minimax polynomial, and deliver the same or better accuracy with significantly fewer operations.
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Do you know of good resource for how to compute minimax polynomials that approximate transcendental functions? My Google foo appears to be failing me.
Re:Implementing Advanced Math Functions
by stephencanon on Wednesday April 25, 2012 @01:31PM
(#3890083)
The standard approach to minimax approximations is called the "Remez Exchange Algorithm" (or Remez algorithm, or Remes algorithm). It can be fussy, however, and often requires a knowledgeable user to product good results, which is why Chebyshev and Cathedory-Fejer approximants are often used instead -- they are very nearly as good, and much easier to compute.