| Course Unit Code | 230-0261/01 |
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| Number of ECTS Credits Allocated | 10 ECTS credits |
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| Type of Course Unit * | Choice-compulsory |
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| Level of Course Unit * | Third Cycle |
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| Year of Study * | |
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| Semester when the Course Unit is delivered | Winter, Summer Semester |
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| Mode of Delivery | Face-to-face |
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| Language of Instruction | Czech |
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| Prerequisites and Co-Requisites | Course succeeds to compulsory courses of previous semester |
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| Name of Lecturer(s) | Personal ID | Name |
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| KRE40 | doc. RNDr. Pavel Kreml, CSc. |
| STA50 | RNDr. Jana Staňková, Ph.D. |
| Summary |
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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. |
| Learning Outcomes of the Course Unit |
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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.
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| Course Contents |
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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.
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| Recommended or Required Reading |
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| Required Reading: |
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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
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Přikryl,P.: Numerické metody matematické analýzy. SNTL, Praha 1985.
Ralston,A.: Základy numerické matematiky. Academia, Praha 1976.
Vitásek,E.: Numerické metody. SNTL, Praha 1987.
Gerald,F.-Wheatley,P.: Applied Numerical Analysis. Addison Wesley 1994.
Stoer,J. - Bulirsch,R.: Introduction to Numerical Analysis. Springer-Verlag, New
York 1993. |
| Recommended Reading: |
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| http://mdg.vsb.cz/portal/nm/nm.pdf |
| http://mdg.vsb.cz/portal/nm/nm.pdf |
| Planned learning activities and teaching methods |
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| Seminars, Individual consultations, Other activities |
| Assesment methods and criteria |
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| Task Title | Task Type | Maximum Number of Points
(Act. for Subtasks) | Minimum Number of Points for Task Passing |
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| Examination | Examination | | |