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from Part II - Constructive Approximation Theory
Published online by Cambridge University Press: 29 September 2022
The best polynomial approximation in a weighted least squares sense is studied in this chapter. The essential notion of orthogonal polynomials, and their properties are analyzed. These are, first of all, used to show existence, uniqueness, and convergence of a least squares best approximation.This motivates the introduction of generalized Fourier series. The issue of uniform convergence of least squares approximations for smooth functions is then studied.
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