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Course, academic year 2018/2019
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Nonlinear Numerical Algebra II - NNUM121
Title in English: Nelineární numerická algebra II
Guaranteed by: Department of Numerical Mathematics (32-KNM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018
Semester: summer
E-Credits: 6
Hours per week, examination: summer s.:2/2 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: cancelled
Language: Czech
Teaching methods: full-time
Guarantor: doc. RNDr. Jan Zítko, CSc.
Classification: Mathematics > Numerical Analysis
Co-requisite : NNUM021
Interchangeability : NMNV534
Is incompatible with: NMNV534
Is interchangeable with: NMNV534
Annotation -
Last update: T_KNM (28.03.2006)
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.

Literature - Czech
Last update: T_KNM (16.05.2008)

[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 a lecture and a tutorial each week in the auditorium during the whole semester. Tutorials are dedicated for the calculation of examples and short programs. Students cover preparing reports on assigned subjects.

Requirements to the exam -
Last update: ZITKO/MFF.CUNI.CZ (25.04.2008)

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

Syllabus -
Last update: T_KNM (16.05.2008)

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.

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