National Repository of Grey Literature 2 records found  Search took 0.01 seconds. 
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...
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)

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