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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
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Monge property for interval matrices
Černý, Martin ; Hladík, Milan (advisor) ; Zimmermann, Karel (referee)
The thesis is a first survey in the field of interval matrices with Monge prop- erty. We investigate characteristics and properties of two classes of matrices - interval strong and interval weak Monge matrices. We develop a recognition and reconstruction algorithms and study applications in combinatorial problems and in a problem connected with computational geometry.
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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 n-dimensional 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
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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
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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
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Cooperative interval games
Bok, Jan ; Hladík, Milan (advisor) ; Valla, Tomáš (referee)
In this thesis, we study cooperative interval games, a generalized model of cooperative games in which worth of every coalition corresponds with a closed interval representing all possible outcomes of their cooperation. We give a brief introduction into classical cooperative games, interval analysis and finally introduction to cooperative interval games with focus on selections, that is on all possible outcomes of interval game with no additional uncertainty. We introduce new selection-based classes of interval games and prove their characterizations and relation to existing classes. We show a new results regarding core and imputations. We introduce a definition of strong imputation and core and examine a problem of equality of two different versions of core -- the main stability solution of cooperative interval games. Finally, we make some new remarks on Shapley value of interval games.
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Overdetermined systems of interval linear equations
Horáček, Jaroslav ; Hladík, Milan (advisor) ; Ratschan, Stefan (referee)
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
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