Syllabus
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.
Annotation
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.