
Interval linear and nonlinear systems
Horáček, Jaroslav ; Hladík, Milan (advisor) ; Garloff, Jürgen (referee) ; Ratschan, Stefan (referee)
First, basic aspects of interval analysis, roles of intervals and their applications are addressed. Then, various classes of interval matrices are described and their relations are depicted. This material forms a prelude to the unifying theme of the rest of the work  solving interval linear systems. Several methods for enclosing the solution set of square and overdetermined interval linear systems are covered and compared. For square systems the new shaving method is introduced, for overdetermined systems the new subsquares approach is introduced. Detecting unsolvability and solvability of such systems is discussed and several polynomial conditions are compared. Two strongest condi tions are proved to be equivalent under certain assumption. Solving of interval linear systems is used to approach other problems in the rest of the work. Computing enclosures of determinants of interval matrices is addressed. NP hardness of both relative and absolute approximation is proved. New method based on solving square interval linear systems and Cramer's rule is designed. Various classes of matrices with polynomially computable bounds on determinant are characterized. Solving of interval linear systems is also used to compute the least squares linear and nonlinear interval regression. It is then applied to real...


Game theory as a confict and cooperation theory
Horáček, Jaroslav ; Černý, Karel (advisor) ; Šubrt, Jiří (referee)
The main focus of this work is the relation between sociology and mathematics, especially the relation between sociological theories of conflict and cooperation and the game theory. In the work four general theories of conflict (and coopera tion) are introduced  theory by John Rex, Kenneth Boulding, Louis Kriesberg and František Znebejánek. Each is accompanied by a critical review. Next, the formal game theory is introduced. The main effort is to shed new light on game theoretic concepts known in sociology and introduce some of the less known ones. The text is focused on the main ideas and explanation without mathematical for malism. Historical relation between sociology and game theory is discussed. Also some topics that are not well handled in game theory from sociological point of view are further elaborated  assumption of rationality, definition of utility and preference, assumption of general knowledge etc. There are also topics from mathematics and informatics slowly penetrating sociology  computer simulation, prediction, that we also discuss. The possible modifications and merit of game theory for sociology is also included. Inspired by the previous theories, at the end of this work a new theoretic model of conflict and cooperation is introduced, which tries to overcome some imperfections of the...


Application of Branch and Bound Approach to Parametric Interval Linear Systems
Szabó, Adam ; Horáček, Jaroslav (advisor) ; Rada, Miroslav (referee)
This work is focused on parametric interval linear systems. By using branch and bound method and various pruning conditions, we first obtained their solution and then described it more precisely with ndimensional boxes. We were acquainted with the basic concepts of intervals and linear systems. Subsequently, we processed the boxes obtained by multiple methods to opti mize their number. Part of the work is also a comparison of various pruning conditions on parametric systems with the different number of parameters. Finally, our algorithms were implemented into the Lime interval package with the possibility of simple visualization of the obtained solutions. 1


Overdetermined systems of interval linear equations
Horáček, Jaroslav ; Hladík, Milan (advisor)
This work is focused on overdetermined systems of interval linear equati ons. First part consists of introduction to interval arithmetics and interval linear algebra and basic theory of interval linear systems. In the second part various methods for solving overdetermined interval linear systems are de scribed. By solution of overdetermined interval system we mean union of all solutions of all subsystems. Known and our variants of algorithms are discussed. We introduce our subsquare method. All mentioned methods are implemented in one toolbox for Matlab. Methods are tested on solvable and unsolvable overdetermined systems. For solvable systems we test solution enclosure, time and special features of methods. For unsolvable systems we test detection of unsolvability. At the end of this work we provide basic in troduction to Intlab. 1


Determinants of Interval Matrices
Matějka, Josef ; Horáček, Jaroslav (advisor) ; Hladík, Milan (referee)
This work focuses on the determinants of interval matrices. After a short introduction into interval arithmetics, the works focus on time complexity of computation tight enclosures of interval determinants, we show what complexity class this problem belongs to and how hard is approximation with relative and absolute error. Next chapter works with various preconditions of a matrix, which could lead to better results. After we analyse preconditioning of matrices we show several methods for computing determinants, starting with Gauss elimination, en ding method using Cramer's rule. We also ponder about special cases of matrices like symmetric, tridiagonal and Toeplitz. At the end we test shown methods. 1


Estimating data with use of interval analysis
Pelikánová, Petra ; Horáček, Jaroslav (advisor) ; Černý, Michael (referee)
This work is focused on estimating interval data by real functions and interval functions. It presents possibilistic and necessity models of interval regression and compares its strong and week formulations. Further we describe algorithms of linear and nonlinear estimation. The application part is based on demonstration of tolerance method and subtracting tolerance method analysing real cases. 1


Psychologicallyplausible and connectionismfriendly implementation of longterm memory
Milota, Martin ; Horáček, Jaroslav (advisor) ; Bálek, Martin (referee)
In recent decades, the influence and sophistication of connectionist systems has soared. The fields of their applications are countless  image re cognition, data mining, robotics, and many more. A part of the thesis focuses on commonly adopted distributed data representations suitable for connectionist systems, devising an extension and testing its usefulness. The goal of the thesis is to use these extensions to design and implement a model of the longterm memory based on a prevalent psychological theory.


Visualisation of interval data
Mečiar, Martin ; Horáček, Jaroslav (advisor) ; Rada, Miroslav (referee)
The thesis is focused on visualisation, comparison and modification of outputs of interval solvers for solving a continuous constraint satisfaction problem. The author's designed solution for the approximation of outputs of solvers is presented in the thesis. The approximation of outputs of solvers is transformed into the problem of visual reallocation of the sets of outputs of solvers on a finer level than interval box level. Main part of the thesis is the program on added CD that allows visualisation, comparison and modification of outputs of interval solvers. The program is written in C++, but can be compiled as a MEX file for MATLAB. A user documentation and a technical documentation for the program are included in the thesis. The thesis shows several examples of program output in the devoted chapter. Powered by TCPDF (www.tcpdf.org)


A Chapter of the Historiography of Art History and Heritage Preservation. František X. Beneš (1820  1888).
Horáček, Jaroslav ; Konečný, Lubomír (advisor) ; Biegel, Richard (referee)
The origins of heritage conservation in Czech lands are usually dated back to the year 1850 when the Central Commission for Research and Conservation of Architectural Heritage (CentralCommission für Erforschung und Erhaltung der Baudenkmalen) was founded in Vienna. In the years 18541855, fourteen conservators were assigned to the Bohemian area whose job was to search for and describe heritage sites and they also were to initiate their repairs. One of those fourteen conservators was one  still rather unbeknown  František X. Josef Beneš (18161888), conservator of Čáslav county, with whose life and work this paper is concerned. He was born into a family of an establishment bureaucrat Josef Alois Beneš in Český Dub, however, soon the family moved to Osek u Rokycan. Having graduated from grammarschool he continued studying at Prague Polytechnic school where he focused on chemistry and sugar industry. He started as a sugar industry adjunct in Dobrovice and later he was moved to Suchdol u Kutné Hory to act as a manager of a local sugar factory. Having helped František Alexander Heber with his work Böhmens Burgen, Vesten und Bergschlösser to whom he gave valuable data about many a building in Kutná Hora area, Beneš himself began to be interested in conservation. In the 1840'swe can already find Beneš...


A tool for evaluation of different methods for solving nonlinear equations
Do Manh, Tuan ; Mikula, Tomáš (advisor) ; Horáček, Jaroslav (referee)
The objective of this work is to create a tool for solving nonlinear equations using numeric methods. It uses both slow working methods, such as bisection method or regula falsi method, and fast working methods, such as Newton's method. The Newton's method, while fast, can be very problematic in certain scenarios. It does not always converse to the root of the equation. That is why in this work, I try to implement modified methods, which attempt to deal with the imperfections of the Newton's method. The program is suppose to be a good tool for comparing and evaluating the efficiency of each methods in different situations.
