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Interval solver for nonlinear constraints
Garajová, Elif ; Hladík, Milan (advisor) ; Pergel, Martin (referee)
The thesis is focused on the Sivia algorithm (Set Inverter via Interval Ana- lysis) designed for solving a continuous constraint satisfaction problem using interval methods and propagation techniques. Basic properties of the algorithm are derived, including the correction of its presented complexity bound. Some improvements concerning the testing of constraint satisfaction and optimiza- tion of the number of interval boxes describing the solution are proposed. The thesis also introduces contractors used to enhance the effectivity of the Sivia algorithm by reducing the interval boxes processed. Presented algorithms were implemented in a solver for nonlinear constraints with a simple visualization of the result using the Matlab language. A comparison of basic contractors on specific examples is given.
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Game theory and poker
Schmid, Martin ; Hladík, Milan (advisor) ; Zimmermann, Karel (referee)
This thesis introduces the basic concepts of the game theory. Necessary models and solution concepts are described. Follows the summary of the computational complexity of these concepts and corresponding algorithms. Poker is formalized as one of the game theory game models. State of the art algorithms for the ex- tensive form games are explained with the application to the Poker. The thesis also introduces the Annual Computer Poker Competition and participating pro- grams. Finally, new result about the extensive form games with many actions is presented. Keywords: Game theory, Poker, Nash equilibrium, Extensive form games
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Linear algebra algorithms visualization
Jakubík, Miroslav ; Pangrác, Ondřej (advisor) ; Hladík, Milan (referee)
This text focuses on problems of implementation of basic linear algebra algorithms. These algorithms are not too complicated, but there is a certain problem of using extremely huge or extremely small numbers which are not comprehensible to the human. Thus, in case of displaying intermediate outcomes, it is better when calculations are made human-like.
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Interval linear systems with linear dependencies
Král, Ondřej ; Hladík, Milan (advisor) ; Rada, Miroslav (referee)
The main problem discussed in this thesis is about finding an enclo- sure of the solution set of an interval linear system with linear dependencies. We get familiar with definitions from interval arithmetic and analysis. Then we extend them to matrices and linear systems, where we introduce several modern approaches to finding an enclosure and divide them thematically. Most of them are implemented in MATLAB using INTLAB library. We compare their precision and computational time on Toeplitz, symmetric and random matrices. For depen- dencies we design our memory saving representation. The results are interpreted and the final function, which can compute either fast, sharp or memory efficient, is build on individual methods. Powered by TCPDF (www.tcpdf.org)
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Scramble simulator
Šindelář, Ondřej ; Bílý, Tomáš (advisor) ; Hladík, Milan (referee)
The work aims to implement a graphic game simulating motocross ride. The player controls a motorbike rider and tries to get him from start to nish as quickly as possible. He has to collect checkpoints laid out along a track without striking his head against the ground. Tracks composed of polygons can be created and edited in included track editor. In addition to single-player game there are also four di erent multiplayer game modes to be played on one or mulitple computers. It is possibile to replay previously saved ride recordings. The scene is displayed as a side view and is rendered using OpenGL library. The program is implemented on Win32 platform.
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Convex functions and their generalization
Krtek, Jiří ; Hladík, Milan (advisor) ; Červinka, Michal (referee)
In the present work we study properties and relations between convex functions and their generalizations. We commence with definition of convex functions and we get to differentiability and searching for extreme points through basic properties as continuity.We continue with quasiconvex, explicitly quasiconvex and pseudoconvex functions. Through their definitions and basic properties we get to relations between them and convex functions. We can find even theorems about composition of these generalizations here, which enable us easier to find, whether given composite function is (explicitly) quasiconvex or pseudoconvex. This work also contains a section dedicated to minimalization of these generalizations. There are mentioned some other generalizations of convexity at the conclusion of this work, which aren't analyzed so much.
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Speciální třídy P-matic v intervalovém prostředí
Lorenc, Matyáš ; Hladík, Milan (advisor) ; Zeman, Peter (referee)
This work focuses on generalizing some easily recognizable subclasses of P-matrices into interval settings, including some results regarding these classes. Those classes are those of B-matrices, doubly B-matrices and BR π -matrices. We derive characterizations, some necessary conditions and sufficient ones, plus we introduce some of their properties, such as are the closure ones and a few conditions the entries of such matrices satisfy. Then we proceed to state a way to generate instances of some of these interval matrix classes. 1
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Preconditioning and regularity of symmetric interval matrices
Vigilev, Pavel ; Hladík, Milan (advisor) ; Horáček, Jaroslav (referee)
In this thesis we observed different approaches to construct a preconditioner for sy- mmetric interval matrices. Using these preconditioners we described and implemented methods for testing regularity of these matrices and compared efficiency of described algorithms. After that we observed different methods for estimating eigenvalues of this class of matrices. Also we constructed such method that uses any testing regularity me- thod for filtering an input interval. After that we compared efficency of these methods on different classes of matrices. All algorithms we implemented using MATLAB with the IntLab library. Comparing numerical results we concluded that the way to test regula- rity of symmetric interval matrix based on the sufficient condition for regularity with standard preconditioner is the most efficient one among the algorithms we implemented. The constructed method for estimating eigenvalues based on testing regularity gives very accurate result because of its iterativity, but it seems to be very slow comparing to other methods which give similar accuracy. 1
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Production of plough share screw
Hladík, Milan ; Jopek, Miroslav (referee) ; Forejt, Milan (advisor)
The bachelor's thesis presents a design of plow screw production technology used to attach the blade to the plow frame. The screw is made of structural steel 14,140, in a production series of 120,000 pcs / year. From the possible technologies, the technology of volume cold forming was chosen. From the literature sources of the issue of volume cold forming, the optimal procedure of screw production was proposed. With the help of design, technological and control calculations, a machine was designed and subsequently a production tool, for which drawing documentation was prepared. With the help of technical - economic evaluation, the costs of component production were compared using volume forming and machining.
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