MA018 Numerical Methods

Fakulta informatiky
podzim 2018
Rozsah
2/2/0. 4 kr. (plus ukončení). Ukončení: zk.
Vyučující
Mgr. Jiří Zelinka, Dr. (přednášející)
RNDr. Veronika Eclerová, Ph.D. (cvičící)
Garance
prof. RNDr. Jan Slovák, DrSc.
Fakulta informatiky
Dodavatelské pracoviště: Ústav matematiky a statistiky – Ústavy – Přírodovědecká fakulta
Rozvrh
St 8:00–9:50 B204
  • Rozvrh seminárních/paralelních skupin:
MA018/01: Po 17. 9. až Po 10. 12. Po 14:00–15:50 A219, J. Zelinka
Předpoklady
Differential calculus of functions of one and more variables. Basic knoledge of linear algebra-theory of matrices and solving systems of linear equations.
Omezení zápisu do předmětu
Předmět je nabízen i studentům mimo mateřské obory.
Mateřské obory/plány
předmět má 16 mateřských oborů, zobrazit
Cíle předmětu
This course together with the course Numerical Methods II provides complete explanation of numerical mathematics as the separate scientific discipline. The emphasis is given to the algorithmization and computer implementation. Some examples with graphical outputs help to explain even some difficult parts.
Výstupy z učení
At the end of course students should be able to apply numerical methods for solving practical problems and use these methods in other disciplines e.g. in statistical methods.
Osnova
  • 1. Error analysis: absolute and relative error, representation of numbers, error propagation
  • 2. Iterative methods for solving of nonlinear equations: general iterative method, order of the convergence, Newton method and its modifications
  • 3. Direct methods for solving systems of linear equations: methods based on Gaussian elimination, methods for special matrices
  • 4. Iterative methods for solving of systems of linear equations: general construction of iterative methods, Jacobi method, Gauss-Seidel method
  • 5. Solving of systems of nonlinear equations: Newton method
  • 6. Interpolation and approximation: polynomial and piece-wise polynomial interpolation, curve approximations, subdivision schemes, least squares method
  • 7. Numerical differentiation: differentiation schemes
  • 8. Numerical integration: methods based on interpolation, Monte Carlo integration
Literatura
    doporučená literatura
  • NOCEDAL, Jorge a Stephen J. WRIGHT. Numerical optimization. 2nd ed. New York: Springer, 2006, xxii, 664. ISBN 1493937111. info
  • MATHEWS, John H. a Kurtis D. FINK. Numerical methods using MATLAB. 4th ed. Upper Saddle River, N.J.: Pearson, 2004, ix, 680. ISBN 0130652482. info
  • BURDEN, Richard L. a J. Douglas FAIRES. Numerical analysis. 6th ed. Pacific Grove, Calif.: Brooks/Cole, 1997, xiii, 811. ISBN 0534955320. info
  • STOER, J. a R. BULIRSCH. Introduction to numerical analysis. 1. vyd. New York - Heidelberg - Berlin: Springer-Verlag, 1980, 609 s. IX. ISBN 0-387-90420-4. info
Výukové metody
Lectures: 2 hours weeky - theoretical preparation, 2 hours weekly - class excercise.
Theoretical exercise (1 hour) is focused on solving of problems by methods presented in the lecture, practical exercise (1 hour) in a computer room is aimed at algoritmization and programming of presented numerical methods.
Metody hodnocení
Written exam and work during the semester - 30 points together.
Assessment of the course:
more then 27 points - A
more then 24 points - B
more then 21 points - C
more then 18 points - D
15 points and more - E
less then 15 points - F
Vyučovací jazyk
Angličtina
Další komentáře
Předmět je vyučován každoročně.
Předmět je zařazen také v obdobích podzim 2017, podzim 2019, podzim 2020, podzim 2021, podzim 2022, podzim 2023, podzim 2024.