Minimax approximation algorithm: Difference between revisions

Revision as of 16:22, 3 September 2012

Revision as of 16:23, 3 September 2012

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==Polynomial approximations==

The conditions for a best appromation are particularly simple if the function p(''x'') is restricted to polynomials less than a stated degree ''n''.<ref name="powell" /> The [[Weierstrass approximation theorem]] states that every continuous function defined on a closed interval [a,b] can be uniformly approximated as closely as desired by a polynomial function.<ref name="phillips" />

Polynomial expansions such as the [[Taylor series]] expansion are often convenient for theoretical work but less useful for practical applications. For practical work it is often desirable to minimize the maximum absolute or relative error of a polynomial fit for any given number of terms in an effort to reduce computational expense of repeated evaluation.