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Nonlinear Numerical Algebra I - NNUM021

Title:	Nelineární numerická algebra I
Guaranteed by:	Department of Numerical Mathematics (32-KNM)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2018
Semester:	winter
E-Credits:	6
Hours per week, examination:	winter s.:2/2, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	cancelled
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	doc. RNDr. Jan Zítko, CSc.
Classification:	Mathematics > Numerical Analysis
Interchangeability :	NMNV501
Is co-requisite for:	NNUM121
Is incompatible with:	NMNV501
Is interchangeable with:	NMNV501

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Annotation -

Last update: T_KNM (17.05.2008)

Methods for minimizing a functional. Computing roots of a polynomial.

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 polynomial 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 the lecture with a tutorial each week in the auditorium during the whole semester.Tutorials are dedicated for the calculation of examples.

Requirements to the exam -

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

Exam of the lecture material at the end of semester. A control of assigned examples.

Syllabus -

Last update: T_KNM (16.05.2008)

First and second derivative of an operator. Convex functionals. Rates of convergence. Introduction into basic optimization methods.

Line search method, basic properties, choice of directions vectors, choice of the stepsize. Global convergence of line search method. Estimate of the rate of convergence. Practical algorithms.

Conjugate gradient methods, global convergence. Conjugate gradient method for a quadratic functional. Restarted conjugate gradient method for a nonquadratic functional, estimate of the rate of convergence.

Chebyshev polynomials.

Laguerr's method for calculation of roots of a polynomial.

Entry requirements -

Last update: T_KNM (16.05.2008)

Fundamental knowledge of mathematical analysis and algebra.