# Markov criterion

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for best integral approximation

A theorem which in some cases enables one to give effectively the polynomial and the error of best integral approximation of a function . It was established by A.A. Markov in 1898 (see ). Let , , be a system of linearly independent functions continuous on the interval , and let the continuous function change sign at the points in and be such that If the polynomial has the property that the difference changes sign at the points , and only at those points, then is the polynomial of best integral approximation to and  For the system on , can be taken to be ; for the system , , can be taken to be ; and for the system , , one can take .

How to Cite This Entry:
Markov criterion. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Markov_criterion&oldid=17793
This article was adapted from an original article by N.P. KorneichukV.P. Motornyi (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article