Terminated in academic year 2012/2013
Mathematical statistics and data analysis
| Type of study | Doctoral |
|---|---|
| Language of instruction | Czech |
| Code | 714-0951/02 |
| Abbreviation | MSAD |
| Course title | Mathematical statistics and data analysis |
| Credits | 10 |
| Coordinating department | Department of Mathematics and Descriptive Geometry |
| Course coordinator | Mgr. Marcela Rabasová, Ph.D. |
Subject syllabus
1st Approximation methods: Formulation of problems and types of approximations. Polynomial interpolation. Interpolation using B-splines, beta-splines and ni-splines. Shape properties: the non-negativity, convexity and monotonicity.
2nd Approximation of curves and surfaces: Ferguson, Bezier and Coons curves.
Interpolation for surfaces using meshesand edges. Cladding.
3rd Fourier transform and its application: continuous and discrete Fourier
transform. FFT algorithm. Windowed transform, time-frequency analysis.
4th Wavelet transform: interpretation. Wavelets as function. Multiresolution analysis. Wavelet spaces. Calculations with wavelets.
5th Application 1: Smoothing algorithms based on Fourier transform and on
minimizing properties of splines. Data compression.
6th Application 2: The numerical solution of differential equations using splines and wavelets. Shape properties of solutions.
7th Application 3: Algorithms for solving linear systems based on Fourier and wavelet transforms.
2nd Approximation of curves and surfaces: Ferguson, Bezier and Coons curves.
Interpolation for surfaces using meshesand edges. Cladding.
3rd Fourier transform and its application: continuous and discrete Fourier
transform. FFT algorithm. Windowed transform, time-frequency analysis.
4th Wavelet transform: interpretation. Wavelets as function. Multiresolution analysis. Wavelet spaces. Calculations with wavelets.
5th Application 1: Smoothing algorithms based on Fourier transform and on
minimizing properties of splines. Data compression.
6th Application 2: The numerical solution of differential equations using splines and wavelets. Shape properties of solutions.
7th Application 3: Algorithms for solving linear systems based on Fourier and wavelet transforms.
Literature
Dummer R. M.: INTRODUCTION TO STATISTICAL SCIENCE. VŠB-TU Ostrava 1998; ISBN 80-7078-497-0
Doporučená literatura
Radim Briš, Petra Škňouřilová. STATISTICS I. VŠB - Technical University of Ostrava, Ostrava 2007.