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Interval Methods - NOPT051

Title:	Intervalové metody
Guaranteed by:	Department of Applied Mathematics (32-KAM)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2023
Semester:	winter
E-Credits:	5
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:	taught
Language:	Czech, English
Teaching methods:	full-time
Teaching methods:	full-time
Additional information:	https://kam.mff.cuni.cz/~hladik/IA/

Guarantor:	prof. Mgr. Milan Hladík, Ph.D.
Class:	Informatika Mgr. - volitelný
Classification:	Informatics > Optimalization
Is incompatible with:	NOPX051
Is interchangeable with:	NOPX051

Opinion survey results Examination dates WS schedule Noticeboard

Annotation -

Last update: prof. Mgr. Milan Hladík, Ph.D. (07.04.2016)

Interval computations provide rigorous bounds for numerical output. For this reasons, it is used in validated computing with floating-point arithmetic, e.g. in computer-aided proofs of famous math conjectures (The Kepler Conjecture, The double bubble problem etc.). It gives verified solutions in solving (non)linear systems of equations and in global optimization. Remark: The course can be tought once in two years.

Course completion requirements -

Last update: prof. Mgr. Milan Hladík, Ph.D. (07.10.2019)

To obtain credits for tutorials, students need to carry out a certain number of homeworks.

More details can be found at web pages:

http://kam.mff.cuni.cz/~hladik/IA

Literature -

Last update: T_KAM (04.05.2011)

E. Hansen, G.W. Walster: Global optimization using interval analysis, Marcel Dekker, 2004.

M. Fiedler et al.: Linear optimization problems with inexact data, Springer, 2006.

L. Jaulin et al.: Applied interval analysis, Springer, 2001.

R.E. Moore, R.B. Kearfott, M.J. Cloud: Introduction to interval analysis, SIAM, 2009.

A. Neumaier: Interval methods for systems of equations, Cambridge University Press, 1990.

A motivational movie:

http://www-sop.inria.fr/coprin/logiciels/ALIAS/Movie/movie_undergraduate.mpg

Requirements to the exam -

Last update: prof. Mgr. Milan Hladík, Ph.D. (07.10.2019)

Examination has the oral form. The requirements correspond to the contents presented at the lectures.

Syllabus -

Last update: T_KAM (04.05.2011)

Interval linear algebra:

interval linear systems of equations and inequalities

(description, complexity, methods),

regularity of interval matrices,

eigenvalues of interval matrices.

(Interval) nonlinear systems of equations.

Interval linear programming.

Global optimization using interval analysis.