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Numerical approximation of matrix eigenvalues
Pres, Jiří ; Zatočilová, Jitka (referee) ; Tomášek, Petr (advisor)
This work deals with numerical methods for the approximation of matrix eigenvalues, which is~a~key problem in many fields of science and technology. Main goal of the thesis is to get to know with several basic algorithms, such as power methods and the QR decomposition. Further to show these algorithms on examples and to compare achieved results. All described algorithms are processed in MATLAB scripts and attached in the appendix. After testing described methods, summary was created regarding their effective usage.
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Solving methods of systems of linear equations
Šotolová, Petra ; Jančařík, Antonín (advisor) ; Novotná, Jarmila (referee)
My bachelor's thesis is focused on methods for solving systems of linear equations. Its aim is to explain the application of these methods for solving systems of linear equations and to assign advantages and the type of system for which each method is advantageous. The thesis should be suitable for elementary and secondary school students, university students, as well as individuals not studying mathematics. It describes substitution method, addition method, comparison method, graphical method, Gaussian elimination, Gauss-Jordan elimination, inverse matrix and Cramer's rule and their application in solving systems of two or more linear equations with two or more unknowns. It includes a general explanation and a specific procedure with examples, advantages and disadvantages of each method, and types of systems for which the method would be used. The thesis examines the number of solutions of systems of equations depending on the form of the system. It also explains basic concepts and provides simplified definitions of the terms used.
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Analytic representation of affine transformations in the plane
Horáčková, Blanka ; Beran, Filip (advisor) ; Zamboj, Michal (referee)
The thesis deals with three main topics - isometric, similar, and affine transformations of the plane from the point of view of analytic geometry. In the first chapter, the most basic concepts are recalled, which will be subsequently dealt with throughout the thesis. The second chapter focuses on identical transformations. Here, we find an analytic representation of this transformation in matrix and complex forms. The third chapter focuses on similar transformations. The central point is then the decomposition of similarity into identity and identicalness, where knowledge of both similarities and identities are combined. The last chapter focuses on affinities. This chapter is not so theoretical anymore but focuses mainly on the characteristic elements of affine transformations and examples. This work's important and beneficial factor is the solved examples, supplemented by several figures. The work is intended primarily for mathematics students as a study material. However, it may also be used by secondary school teachers to supplement the secondary school curriculum.
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Computation of the eigenvalues and eigenvectors of Hermitian matrix
Štrympl, Martin ; Bohrn, Marek (referee) ; Fujcik, Lukáš (advisor)
This project deals with computation of eigenvalues and eigenvectors of Hermitian positive-semidefinite complex square matrix of order 4. The target is an implementation of computation in language VHDL to field-programmable gate array of type Xilinx Zynq-7000. This master project deals with algorithms used for computation of eigenvalues and eigenvectors of positive-semidefinite symmetric real square and positive-semidefinite complex Hermitian matrix and the analysis of algorithms by AnalyzeAlgorithm program assembled for this purpose. The closing part of this project describes implementation of the computation into field-programmable gate array with use of IP core Xilinx® Floating-Point \linebreak Operator and SVAOptimalizer, SVAInterpreter and SVAToDSPCompiler programs.
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Use of FRP Composites as Reinforcing Material for Concrete
Kratochvílová, Denisa ; Prokeš,, Jan (referee) ; Bodnárová, Lenka (advisor)
Because FRP composites have high fiber strength and good durability, they are increasingly used for repairs, modernisation and reconstruction of concrete structures. In practice, however there is a risk of premature separation of FRP reinforcement from concrete. This can be avoided by appropriate selecting the fibers and the matrix and the appropriate shape of the reinforcement. The actual materials and consistency of FRP reinforcement with concrete are also covered by this diploma thesis.
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Matrix headphone amplifier for studio monitoring
Štěrba, Václav ; Petržela, Jiří (referee) ; Kratochvíl, Tomáš (advisor)
This bachelor´s thesis describes the design of a matrix headphone amplifier for studio monitoring. The proposed amplifier is a purpose-built device to be used in studio sound recording for the mixing of multiple audio channels directed to the interpreters´or performers´ headsets. The device is basically composed of the following parts: An input section for the audio line, a mixing section which secures the setting of individual input levels for each output, an amplifier section allowing the setting of the output signal level for each output, and an output section enabling the connection of headphones. The equipment utilizes a connection to a multi-channel audio signal bus; this bus also provides for remote power supply to all the connected devices. The solution described in the thesis can be defined as alternative monitoring that facilitates quick and easy connection of a required number of monitoring points (in other cases, such monitoring is usually realized by means of individual small mixing consoles).
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Mechanical properties of fiber reinforced composites for automotive applications
Bayer, Adam ; Žídek, Jan (referee) ; Jančář, Josef (advisor)
Bachelor’s thesis deals with studying mechanical features of fiber composites. As a matrix was chosen PMMA and as reinforcement was chosen glass fabric. Theoretical part sums up contemporary issues of polymer composites in automotive industry such as their production techniques and methods of impregnation. In experimental part were prepared samples by block polymerization of 30 % solution PMMA in monomer with initiator by 65° Celsius warmth oath, when was fabric directly unfolded in pre-polymer solution. On these samples were executed tensile tests by testing device Zwick and these samples were compared with results of theoreticaly calculated values.
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Manufacturing Process and Applications of Composite Materials for buses parts
Rusek, Jan ; Julišová, Martina (referee) ; Němec, Karel (advisor)
The aim of the bachelor’s thesis is the evaluation and demonstration of the usability of composite materials in the bus industry. The first chapter provides an overview of selected types of composite materials, basic classification, description of their parts and demonstrations of methods of production. The second part of the bachelor’s thesis is focused on the evaluation of the advantages and disadvantages of using composite materials. The last part is focused on the producion of the sample from fiberglass.
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Selected Extensions of the Albegraic System Octave
Salač, Radek ; Smrčka, Aleš (referee) ; Vojnar, Tomáš (advisor)
This work deals with issues linked to solving system of linear equations in the environment of numerical computer. It describes the fundamental algorithms emphasizing their positive as well as negative sides. The work is devoted to general issues such as time complexity and memory demandingness of given algorithms. In the last part, the process of implementation of selected procedures into the algebraic system Octave is described.
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Design of laminate handlebars for mountain bikes
Hanák, Jiří ; Ševeček, Oldřich (referee) ; Polzer, Stanislav (advisor)
This bachelor’s thesis describes design of laminate handlebars for mountain bikes. The first part describes the mechanical properties of composite materials, with the emphasis on fiber composites. The algorithm for acquiring material characteristics of fiber composite by analytical method is presented. In the next part, it is shown how to control the direction of fibers in lam-inate in the finite element calculations and its impact to resulting stresses in the material. The aim of the last part is design geometry model of laminate handlebars for mountain bikes with following stress – strain analysis by FEM and software ANSYS. The analysis is performed for static loading.
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