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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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Regression analysis and splines
Benko, Milan ; Bašta, Milan (advisor) ; Komárek, Arnošt (referee)
The aim of this Bachelor's thesis is to introduce the basic concepts of regression analysis and subsequently regression splines as parametric models for regression function. I have looked upon the main characteristics of regression splines (coherence, coherence of derivations, the choice of placement and a number of knots). Further on in the thesis I have studied two bases as the examples of regression splines (truncated power basis and B-spline basis). I have also presented a model of natural cubic splines and a suitable basis for its representation has been derived. In the other part of my thesis I have looked upon the use of natural splines in order to increases the appraisal precision of regression function, mean square error formula has been derived and I have been trying to find out and illustrate under what conditions the use of natural splines is applicable. The thesis is complemented with a Monte Carlo Simulation, contextualized into models of splines. The results show that the criteria commonly used for the choice of a model ($\R_{adj}^2$, $PRESS$ statistic, hypothesis testing) do not always enable us to choose the right model in order to achieve the greatest precision of the estimation of regression function. All the calculations are done in R software and are in the electronic attachment....
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Identification of DC motor parameters
Kabelka, Ondřej ; Veselý, Libor (referee) ; Pohl, Lukáš (advisor)
This bachelor´s thesis deals with identification of parameters of the DC motor. An identification program in LabVIEW with data processing in Matlab has been created. After the identification of electrical and mechanical parameters of the motor there are current regulators and velocity regulators designed and implemented in the LabVIEW enviroment as a verification of the correctness of the identification.
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Self-tuning control of electric motor
Havlíček, Jiří ; Blaha, Petr (referee) ; Pohl, Lukáš (advisor)
The diploma thesis deals with the self-tuning PSD controllers. The parameters of the model are obtained by a non-recurring method of least squares. With the assistance of the Matlab/Simulink programme, the individual processes of the PSD controller are compared on a second order system. In the thesis, a simulation of the self-tuning cascade control of PMSM‘s current and speed loop is created. The following part of the thesis covers the implementation of individual algorithms on the dSPACE platform for the real PMSM.
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Statistical problems in Markov chains with applications in finance
Chudý, Marek ; Prokešová, Michaela (advisor) ; Pawlas, Zbyněk (referee)
Title: Statistical problems in Markov chains with applications in finance Author: Marek Chudý Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Michaela Prokešová, Ph.D. Abstract: In this work, we study estimation methods for estimating transition probabilities in Markov chains. We discuss two methods, the first one for com- plete data and the second one for aggregate data. In the second chapter, we will introduce the theory for both methods and show examples of tests of sev- eral hypothesis about transition probabilities. In the last chapter we apply both methods to real data comming from an insurance company. In the last chapter we also present the results of both methods and compare them with each other. Keywords: Markov chains, transition probabilities, maximum likelihood method, least squares method
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Interactive software tools for teaching signal and image processing
Olbert, Jaroslav ; Rajmic, Pavel (referee) ; Mangová, Marie (advisor)
The bachelor’s thesis deals with creating Java applets to support teaching signal and image processing. The theoretical part of the thesis briefly describes the history and advantages of the Java language; subsequently the theories for individual applets and descriptions of the source codes are presented. The practical part consists of the design and creation of applets for linear combinations of images, the least squares method and recommendation of an aiming point on the darts target.
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Kinetics of Inkjet Dyes Degradation
Buteková, Silvia ; Mikula, Milan (referee) ; Klusoň, Petr (referee) ; Veselý, Michal (advisor)
The stability of inkjet print is influenced by a lot of factors. Mutual effects of these factors accelerate the print degradation. The surrounding environment in image stability plays an important role, when the prints degrade especially by the light. The degradation of inkjet prints is presented as a decrease of dye or multiple dyes. It is necessary to know the dye concentration for the dye decrease prediction in the time. This dissertation thesis deals with the study of kinetics and changes in electron and molecular structure of digital photography prints after accelerated ageing tests. The study of resistance of inkjet prints was realized on one type of media using three different sets of inks. Changes in printed colours were measured and evaluated in calibration (by PLS calibration and least squares method). On the basis of calibration the dye decrease prediction of real samples in receiving layer was evaluated. Changes in electron and molecular structure were analysed on KBr pellets by FTIR an UV-Vis spectroscopy.
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