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Approximation Theory and Applications: Course Outline (MAT-607)

Approximation theory is an established field, and my aim is to teach you some of its most important ideas and results, centered on classical topics related to polynomials and rational functions.

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Course Outline

Approximation of periodic functions, the Weirstrass theorem, the Stone-Weierstrass theorems, approximation in normed linear spaces, linear Chebyshev approximation of vector valued functions, Chebyshev polynomials, strong uniqueness and continuity of metric projections, discrete best approximation, algorithms of Remes, moduli of Continuity, direct theorems, converse theorems, approximation by algebraic polynomials, approximation of analytic functions.


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