TOPICS
Search

Minimax Approximation


A minimax approximation g^* to a function f from a prescribed class A minimizes the greatest absolute error over the domain D, so

 ||f-g^*||_infty=inf_(g in A)||f-g||_infty,

where ||h||_infty=sup_(x in D)|h(x)| is the supremum norm. Thus the error is minimized uniformly over D. When A is the class of polynomials of a specified degree, g^* is a minimax polynomial, and it can be computed under suitable conditions by the Remez algorithm.


See also

Absolute Error, Minimax Polynomial, Remez Algorithm, Supremum Norm

Explore with Wolfram|Alpha

References

Cheney, E. W. Introduction to Approximation Theory, 2nd ed. Providence, RI: AMS Chelsea Publishing, 2000.

Referenced on Wolfram|Alpha

Minimax Approximation

Cite this as:

Weisstein, Eric W. "Minimax Approximation." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/MinimaxApproximation.html

Subject classifications