# Mean-square approximation of a function

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An approximation of a function by a function , where the error measure is defined by the formula where is a non-decreasing function on different from a constant.

Let (*)

be an orthonormal system of functions on relative to the distribution . In the case of a mean-square approximation of the function by linear combinations , the minimal error for every is given by the sums where are the Fourier coefficients of the function with respect to the system (*); hence, the best method of approximation is linear.

How to Cite This Entry:
Mean-square approximation of a function. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Mean-square_approximation_of_a_function&oldid=17600
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