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Nonlinear Numerical Algebra for Ph.D. Students II - NNUM232

Title:	Nelineární numerická algebra pro doktorandy II
Guaranteed by:	Department of Numerical Mathematics (32-KNM)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2014 to 2017
Semester:	summer
E-Credits:	6
Hours per week, examination:	summer 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. Petr Tichý, Ph.D.
Class:	DS, vědecko - technické výpočty
Classification:	Mathematics > Numerical Analysis

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Annotation -

Last update: T_KNM (15.01.2007)

Computing roots of a polynomial. Methods for minimizing a functional. Solution of systems of nonlinear equations.

Aim of the course -

Last update: ZITKO/MFF.CUNI.CZ (25.04.2008)

Students learn the most modern methods for minimization of functionals and the solution of systems of nonlinear algebraic equations. Some practical algorithms will be presented.

Literature - Czech

Last update: T_KNM (17.05.2008)

[1] Najzar, K., Zítko, J. : Numerické metody funkcionální analýzy I a II (Numerical methods in functional analysis I and II), SPN, Praha, 1987.

[2] Ortega, J. M., Rheinboldt W.C. : Iterative solution of nonlinear equations in several variables, Academic Press, New York and London, 1970.

[3] Lukšan, L.: Metody s proměnnou metrikou (Variable metric methods), Academia, Praha, 1990.

[4] Lukšan, L.: Numerické optimalizační metody (Numerical optimization methods), Institute of Computer Science, Technical report No. 930 (262 pages), December 2005.

[5] Ralston, A. : Základy numerické matematiky, Academia, Praha 1973.

Teaching methods -

Last update: ZITKO/MFF.CUNI.CZ (25.04.2008)

The course has the lecture with a tutorial each week in the auditorium during the whole semester. Tutorial are dedicated for the calculation of examples and corresponding short programs. Students prepare reports for given subjects.

Requirements to the exam -

Last update: ZITKO/MFF.CUNI.CZ (25.04.2008)

Examination of the lecture material at the end of semester and a control of examples and assigned projects.

Syllabus -

Last update: T_KNM (17.05.2008)

Lehmer-Schur method.

Variable metric methods. Detailed analysis of computational techniques. Global convergence of variable metric methods.

Trust region methods, global convergence, conditions for superlinear convergence. Trust region methods with optimal locally constrained step and the determination of the optimal locally constrained step. Inexact trust region method. Detailed computational algorithms.

Methods for solving system of nonlinear equations.

Entry requirements -

Last update: ZITKO/MFF.CUNI.CZ (25.04.2008)

Fundamental knowledges of mathematical analysis, algebra and programming of MATLAB or FORTRAN.