SubjectsSubjects(version: 964)
Course, academic year 2024/2025
   Login via CAS
Approximation of functions 2 - NMNV568
Title: Aproximace funkcí 2
Guaranteed by: Department of Numerical Mathematics (32-KNM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2024
Semester: summer
E-Credits: 3
Hours per week, examination: summer s.:2/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Additional information: https://www.pozza.me/teaching/20202021/aof2
Guarantor: doc. RNDr. Václav Kučera, Ph.D.
Teacher(s): Stefano Pozza, Dr., Ph.D.
Class: M Mgr. NVM
M Mgr. NVM > Volitelné
Classification: Mathematics > Numerical Analysis
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.
Last update: Kučera Václav, doc. RNDr., Ph.D. (15.01.2019)
Course completion requirements -

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)
Literature -

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)
Requirements to the exam -

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)
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.

Last update: Kučera Václav, doc. RNDr., Ph.D. (12.05.2018)
Entry requirements -

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)
 
Charles University | Information system of Charles University | http://www.cuni.cz/UKEN-329.html