# Element of best approximation

From Encyclopedia of Mathematics

An element in a given set that is a best approximation to a given element in a metric space , i.e. is such that

This is a generalization of the classical concept of a polynomial of best approximation. The main questions concerning elements of best approximation are: their existence and uniqueness, their characteristic properties (see Chebyshev theorem), the properties of the operator that associates with each element the set of elements of best approximation (see Metric projection; Approximately-compact set), and numerical methods for the construction of elements of best approximation.

**How to Cite This Entry:**

Element of best approximation.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Element_of_best_approximation&oldid=18961

This article was adapted from an original article by Yu.N. Subbotin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article