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Introduction to approximation theory of continuous functions in normed linear spaces, with an emphasis on numerical methods for the computation of approximations.
The course deals with problems of polynomial interpolation, minimax approximation, and least squares approximation. Students will test the algorithms practically during the exercise.
Last update: Kučera Václav, doc. RNDr., Ph.D. (05.12.2018)
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It is not necessary to obtain a course-credit before passing the exam.
The course-credit will be granted for the attendance and for a short presentation given during the semester.
The nature of these requirements does not allow a possibility of some additional attempts to obtain the course-credit. Last update: Tichý Petr, doc. RNDr., Ph.D. (06.10.2017)
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M. J. D. Powell, Approximation theory and methods. Cambridge University Press, Cambridge-New York, 1981.
N. L. Trefethen, Approximation Theory and Approximation Practice. Society for Industrial and Applied Mathematics, Philadelphia, PA, 2013.
E. W. Cheney, Introduction to approximation theory. AMS Chelsea Publishing, Providence, RI, 1982.
R. A. DeVore, G. G. Lorentz, Constructive Approximation, vol. 303 of Grundlehren der Mathematischen Wissenschaften,, Springer-Verlag, Berlin, 1993. Last update: Kučera Václav, doc. RNDr., Ph.D. (29.10.2019)
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The exam is oral. Requirements for the oral exam correspond to the syllabus of the course, presented at the lectures. Last update: Tichý Petr, doc. RNDr., Ph.D. (06.10.2017)
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Best approximation in normed linear spaces, approximation operators. Polynomial approximation: Barycentric interpolation formula, Chebyshev interpolant and projection. Minimax approximation, Haar condition, Remez algorithm. Least squares approximation, orthogonal polynomials, periodic functions, uniform convergence, Jackson's theorems. Practical applications: Chebfun, spectral methods, matrix functions. Last update: Kučera Václav, doc. RNDr., Ph.D. (05.12.2018)
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Fundamentals of mathematical analysis and numerical linear algebra. Basic knowledge of the Matlab programming language. Last update: Tichý Petr, doc. RNDr., Ph.D. (02.05.2018)
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