Version 1 (modified by sam, 9 years ago) (diff)


Table of Contents

  1. Example
  2. Download
  3. Tutorial

Remez exchange toolbox

The Remez exchange algorithm is a fast method for approximating functions in a Chebyshev space. The Lol Engine provides its own implementation of the Remez exchange algorithm to find polynomial approximations to real functions. Such polynomials are also known as minimax polynomials.


The following graph shows approximations of sin(x) over [-π, π] using three different polynomials:

  • the Taylor series to the 5th order: x-x³/6+x⁵/120
  • the Taylor series to the 7th order: x-x³/6+x⁵/120-x⁷/5040
  • the minimax polynomial to the 5th order: x-0.1587164x³+0.00585375x⁵

It is obvious that the polynomial found using the Remez method is closer to the sine curve than the Taylor series of same order, and even better than the next order.




Before you start reading the tutorial, I suggest you have a quick look at the Lol Engine real numbers? documentation.

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