11.2.9 Minimax polynomial approximation

The minimax command finds the minimax polynomial approximation of a continuous function on a bounded interval using the Remez algorithm.

• minimax takes three mandatory argument and one optional argument:
  • expr, a univariate expression representing a continuous function.
  • var=a..b, a variable and the interval.
  • n, a positive integer, the degree of the resulting polynomial.
  • Optionally limit=m, where m is a positive integer specifying the number of iterations of the Remez algorithm. (By default, the number of iterations is unlimited.)
• minimax(expr,var=a..b,n ⟨,limit=m ⟩) returns the minimax polynomial approximation of degree n or lower that approximates expr on [a,b]. The largest absolute error of the resulting polynomial will be printed in the message area.

Since the coefficients of p are computed numerically, you should avoid setting n unnecessary high as it may result in a poor approximation due to the roundoff errors.

Example

max. absolute error: 5.85231264871e-06