Least squares approximation with constraints
Authors:
Gradimir V. Milovanović and Staffan Wrigge
Journal:
Math. Comp. 46 (1986), 551565
MSC:
Primary 65D15; Secondary 41A30
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 and Let further be the set of all real polynomials of degree not higher than 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 and We apply the general theory to the functions and , where .
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198608296257
PII:
S 00255718(1986)08296257
Keywords:
Approximation theory,
Gegenbauer polynomials
Article copyright:
© Copyright 1986
American Mathematical Society
