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Chebyshev approximation

Mudde, M.H. (2017) Chebyshev approximation. Master's Thesis / Essay, Science Education and Communication.

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Abstract

In this thesis, Chebyshev approximation is studied. This is a topic in approximation theory. We show that there always exists a best approximating polynomial p(x) to the function f(x) with respect to the uniform norm and that this polynomial is unique. We show that the best approximating polynomial is found if the set f(x) - p(x) contains at least n + 2 alternating points. The best approximating polynomial can be found using four techniques: Chebyshev approximation, smallest norm, economization and an algorithm. For algebraic polynomials in the interval [-1; 1], we assume that an orthogonal projection can be used too. We suppose that approximation of algebraic polynomials in [-1; 1] with respect to the L2-norm with inner product <f; g> = int -1 to1 f(x)g(x)/sqrt(1-x^2) dx and approximation with respect to the uniform norm give the same best approximating polynomial.

Item Type: Thesis (Master's Thesis / Essay)
Degree programme: Science Education and Communication
Thesis type: Master's Thesis / Essay
Language: English
Date Deposited: 15 Feb 2018 08:29
Last Modified: 15 Feb 2018 08:29
URI: http://fse.studenttheses.ub.rug.nl/id/eprint/15406

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