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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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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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Solving interval systems by the least squares method
Tomandl, David ; Hladík, Milan (advisor) ; Hartman, David (referee)
This thesis is describing, comparing and implementing enclosure methods for solving overdetermined system of interval linear equations by the least squares method. Input data of the methods are within given intervals. We describe the structure of the solution set, which is the basis of algorithms for computing interval hull of the solution set. Although computation of the interval hull is NP-hard problem, there exist algorithms which encloses the solution set with less than exponential steps. We are heavily focusing on these algorithms. The solution set can be alternatively characterized as a solution to the symmetric interval system. Therefore the work includes solvers of the symmetric interval system. This thesis contains numerical experiments for comparing the methods. All methods are implemented in Matlab with utilisation of the interval toolbox Intlab. Powered by TCPDF (www.tcpdf.org)
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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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Report on the Last Work by Dr. Erich Nuding
Rohn, Jiří
This is a facsimile copy of a 1994 report on the unpublished last paper by Dr. Erich Nuding. It is being made public here in the hope that even after twenty-two years it may be of interest for researchers working in the area of interval computations because of the intriguing concept of the "fourth modality" which has not been rediscovered during a quarter of century which has elapsed since its original formulation.
Fulltext: content.csg -  PDF
Plný tet: v1235-16 - PDF
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