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Course, academic year 2019/2020
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Interval Methods - NOPT051
Title in English: Intervalové metody
Guaranteed by: Department of Applied Mathematics (32-KAM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2019 to 2019
Semester: winter
E-Credits: 6
Hours per week, examination: winter s.:2/2 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Guarantor: doc. Mgr. Milan Hladík, Ph.D.
Class: Informatika Mgr. - volitelný
Classification: Informatics > Optimalization
Annotation -
Last update: doc. 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: doc. 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:

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:

Requirements to the exam -
Last update: doc. 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.

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