Least squares approximation with constraints

Authors:
Gradimir V. MilovanoviÄ‡ and Staffan Wrigge

Journal:
Math. Comp. **46** (1986), 551-565

MSC:
Primary 65D15; Secondary 41A30

DOI:
https://doi.org/10.1090/S0025-5718-1986-0829625-7

Corrigendum:
Math. Comp. **48** (1987), 854.

MathSciNet review:
829625

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Abstract: In this paper we study two families of functions and , and show how to approximate the functions in the interval . The functions are assumed to be real when the argument is real. We define

*m*such that the polynomials belong to the set if

*m*is even and to the set if

*m*is odd.

We determine the least squares approximation for the function (or ) in the class (or ), with respect to the norm , where the inner product is defined by , with and .

We also consider the general case when *f* is neither an even nor an odd function but and .

Using the theory of Gegenbauer polynomials we obtain the approximating polynomials in the form

We apply the general theory to the functions and , where .

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1986-0829625-7

Keywords:
Approximation theory,
Gegenbauer polynomials

Article copyright:
© Copyright 1986
American Mathematical Society