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The course is a follow-up of the Approximation of functions 1 course and supplements selected important topics in approximation theory that do not fit in the winter course. The focus is especially on the basics of spline functions and
wavelets.
Last update: Kučera Václav, doc. RNDr., Ph.D. (15.01.2019)
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The exam is oral. The examination requirements are given by the topics in the syllabus, in the extent to which they they were taught in course. Last update: Kučera Václav, doc. RNDr., Ph.D. (12.05.2018)
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NAJZAR K., Základy teorie splinů, Univerzita Karlova v Praze, Nakladatelství Karolinum, Praha, 2006.
MICULA G., MICULA S. Handbook of splines, Kluwer Academic Publishers, 1999.
FARIN G., Curves and surfaces for computer aided geometric design, Academic Press, 1990.
NAJZAR K., Základy teorie waveletů, Univerzita Karlova v Praze, Nakladatelství Karolinum, Praha, 2006.
DAUBECHIES I., Ten lectures on wavelets, CBMS-NSF Lecture Notes nr. 61, SIAM , 1992.
TREFETHEN N.L., Approximation Theory and Approximation Practice, SIAM, Philadelphia, PA, 2013.
RIVLIN T.J., An introduction to the approximation of functions, Blaisdell Publishing Co. Ginn and Co., 1969.
CHENEY E.W., Introduction to approximation theory, AMS Chelsea Publishing, Providence, RI, 1982.
https://www.pozza.me/teaching/20202021/aof2 Last update: Pozza Stefano, Dr., Ph.D. (12.02.2021)
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The exam is oral. The examination requirements are given by the topics in the syllabus, in the extent to which they they were taught in course. Last update: Kučera Václav, doc. RNDr., Ph.D. (10.06.2019)
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Spline functions - polynomial splines, basic concepts and definitions. Interpolation and approximation properties. Qualitative properties - monotonicity and convexity preserving. Extremal properties of splines. Smoothing splines. Bézier curves, B-splines, rational B-splines.
Wavelets - Discrete Fourier transform, window Fourier transform, Haar basis, wavelet definition. Wavelet analysis, reconstruction and compression. Daubechies wavelets, 2D wavelets. Approximation properties.
Rational approximation: Interpolation, best approximation, continued fractions, Padé approximation. Last update: Kučera Václav, doc. RNDr., Ph.D. (12.05.2018)
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General knowledge of mathematical analysis. Basic knowledge of functional analysis. Passing the Approximation Theory course is welcome but not necessary. Last update: Kučera Václav, doc. RNDr., Ph.D. (12.05.2018)
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