714-0926/01 – Interpolation and Approximation of Functions (IaAF)

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits10
Subject guarantordoc. RNDr. Pavel Kreml, CSc.Subject version guarantordoc. RNDr. Pavel Kreml, CSc.
Study levelpostgraduateRequirementChoice-compulsory
YearSemesterwinter + summer
Study languageCzech
Year of introduction1997/1998Year of cancellation2012/2013
Intended for the facultiesFMT, FAST, HGF, FS, FEI, USP, FBIIntended for study typesDoctoral
Instruction secured by
LoginNameTuitorTeacher giving lectures
KRE40 doc. RNDr. Pavel Kreml, CSc.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+0
Combined Credit and Examination 0+0

Subject aims expressed by acquired skills and competences

Main study goals: (i) to be acquainted with actual progress in this mathematical discipline, (ii) to extend needed theoretical knowledge with emphasized orientation to its applica-bility, (iii) to increase communication ability of specialists in different branches. With regard to professional orientation of students learning themes modification is offered to fulfill presented aims.

Teaching methods

Seminars
Individual consultations
Other activities

Summary

These lectures deal with methods for constructing approximating functions for any set of data by using polynomial interpolation, least-squares approximation and Chebyshev approximation. There are compared several ways of doing interpolation and there are contrasted these procedures with several ways for fitting imprecise data and for drawing smooth curves. It is shown how can help symbolic algebra computer algebra programs in obtaining interpolating and least-squares polynomials.

Compulsory literature:

Gerald,F.-Wheatley,P.: Applied Numerical Analysis. Addison Wesley 1994. Stoer,J. - Bulirsch,R.: Introduction to Numerical Analysis. Springer-Verlag, New York 1993. Boháč, Zdeněk: Numerical Methods and Statistics, VŠB – TUO, Ostrava 2005, ISBN 80-248-0803-X

Recommended literature:

http://www.studopory.vsb.cz http://mdg.vsb.cz

Way of continuous check of knowledge in the course of semester

E-learning

http://www.studopory.vsb.cz http://mdg.vsb.cz (in Czech language)

Další požadavky na studenta

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Syllabus 1. Kinds of: - dependence and independence of functions, - existence and definiteness of approximating functions, - error of approximation. 2. Polynomial interpolation: -the error estimate of the interpolation, - Lagrangian and Mewton polynomials, - extrapolation, interpolation of rational functions, - choice of points for fitting. 3. Interpolating with a spline functions : - interpolating with a cubic spline, - features of cubic spline, - B-spline curves, - Bezier curves. 4. Orthogonal system of functions: - orthogonal polynomials, - Chebyshev, Hermitov, Gramov polynomials. 5. Least-squares approximations: - the best L2- approximation, least-squares method, - normal equations, solving sets of linear equations, - algorithm of least-squares method, - nonlinear data. 6. Chebyshev approximation: - the best uniform approximation, - algorithm of the method, maximum error.

Conditions for subject completion

Combined form (validity from: 1960/1961 Summer semester, validity until: 2012/2013 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (100) 51
        Examination Examination 100  51
        Exercises evaluation Credit  
Mandatory attendence parzicipation:

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Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner