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Theory of Splines and Wavelets 1 - NNUM016

Title:	Teorie spline funkcí a waveletů 1
Guaranteed by:	Department of Numerical Mathematics (32-KNM)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2013 to 2017
Semester:	winter
E-Credits:	6
Hours per week, examination:	winter s.:2/2, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	not taught
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	doc. RNDr. Václav Kučera, Ph.D.
Classification:	Mathematics > Numerical Analysis
Interchangeability :	NMNV563
Is incompatible with:	NMNV563
Is interchangeable with:	NMNV563

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

Last update: T_MUUK (22.11.2000)

The subject of this course is the treatment of basic properties of spline functions. It contains: interpolation and approximation properties of spline functions, natural and smoothing splines, error estimates and algorithmization. In the exercise, some simple problems are solved on computers.

Aim of the course -

Last update: T_KNM (18.05.2008)

The aim of this course is presenting the theory of spline functions and some their applications. Tutorials contain testing given algorithms on computers.

Literature -

Last update: T_KNM (18.05.2008)

K. Najzar, Základy teorie splinů (Fundamentals of splines theory), skripta (lecture notes), Nakladatelství Karolinum, Praha, 2006

Ch. Micula and S. Micula, Handbook of splines, 1999

G. Farin, Curves and surfaces for computer aided geometric design, 1988

Teaching methods -

Last update: T_KNM (18.05.2008)

The course consists of lectures in a lecture hall and tutorials in a computer laboratory.

Requirements to the exam -

Last update: T_KNM (18.05.2008)

Examination according to the syllabus and tests of given algorithms.

Syllabus -

Last update: T_KNM (18.05.2008)

Polynomial spline functions, basic properties and historical notes.

Construction of local bases. Variational property of the odd-degree splines. B-splines. Periodic, natural, g-splines and L-splines.

Approximation power of splines. Interpolation and smoothing.

Bézier curves and Bernstein approximation.

Spline functions in computer aided geometric design - B-spline curves and surfaces. Spline wavelets. Some application of splines in numerical analysis.

Entry requirements -

Last update: T_KNM (18.05.2008)

Fundamentals of numerical mathematics, mathematical analysis and functional analysis.