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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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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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Interactive Manipulation with 3D Objects with Force Feedbeck
Bělín, Jan ; Chudý, Peter (referee) ; Kršek, Přemysl (advisor)
Physical haptic interaction is added to the modern manipulation with objects in virtual space. In content of this master's thesis the haptic technology is represented by SensAble Phantom Omni device and OpenHaptics toolkit, which is related to the device. Reader is initially introduced into mathematical basics of manipulation and into haptic technology history including current state. The introduction into Openhaptics toolkit follows as well as HDAPI and HLAPI libraries description. As a result of this theoretical basics demo aplications have been created, that show basic and advanced abilities of the Phantom Omni device. Demos represent the functionality of the device as examples integrating well-known elementary physical laws and events.
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Ball screws for the feed system with long stroke
Nováček, Milan ; Novotný, Lubomír (referee) ; Marek, Jiří (advisor)
Master´s thesis is directed for long ball screws of nut. It is here wrote their principle, essential type, parameters and current status of single used components. For this thesis is created at program Microsoft Excel methodical calculating of required parameters ball screws of nut. Another they are investigated status of affect length shaft ball screws, as mode storage, type actuator and possible damping. In last part is solved the design of supports long shaft ball screws and is here proposed conceptual process used supports.
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Enhanced mathematical library for C++
Temel, Aleš ; Macho, Tomáš (referee) ; Petyovský, Petr (advisor)
I create a library for storing matrices and working with matrices in this bachelor’s thesis. In this case, the issues concern mainly so-called sparse matrices. C++ do not provide among the standard libraries tools for easy working with sparse matrices. The most frequent alternative is the application of two-dimensional array (2D array). 2D array may be realized as a double pointer representing the rows and the columns of the matrix. The basic problem is that behavior of 2D array is identical both to the sparse, and to the full non-zero matrix. 2D array ignores the possibility to store matrices more favorable. The library for storing matrices designed by me takes into account the storing of sparse matrices by several different ways. It offers the sparse format CSR (Compressed sparse rows), as well as alternatives to save the specially structured matrices. In the course of creating library the main emphasis first of all I put on the amount of memory that is necessary for storing matrices. Because it is a mathematical library, it contains different functions suitable for working with matrices, such as determinant calculation, inverse matrix calculation and so. When calculate these functions it is necessary to take into account used memory size as well. Intermediate results are stored also in sparse format, and removed as soon as possible after their use. I created also the second library that deals with the floating point numbers stored with greater precision than standard data types like float and double. The size of occupied memory increases according to precision of floating point number.
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Realization of educational problem based on preloaded bolted joint apparatus
Žaba, Tomáš ; Náhlík, Luboš (referee) ; Vaverka, Michal (advisor)
In the master’s thesis an educational task concerning an experimental apparatus for quantity measurement in preloaded bolted joint is realised. In terms of its preparation an innovation of the apparatus leading to an easier and faster pretension realisation was implemented. The educational task for students and also teaching material were produced. The educational task itself consists in experimental confirmation of the relation between the tightening torque and the caused pretension. An FEM model simulating an apparatus flange deformation by given pretension was designed to verify the experiment. The thesis also contains information about the preloaded bolts, pretension elicitation methods and pretension control methods.
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Matrices, Determinant and Body Volume
Šomplák, Radovan ; Hrdina, Jaroslav (referee) ; Vašík, Petr (advisor)
In his thesis describes the basic properties of matrices, determinants and their use in display issues between vector spaces. In the final chapters devoted to determinants and its applications, which indicates the relation between determinants and calculation of volume. Subsequently determinanti describes how to use in calculating the elements using multiple integrals. Another possible application is the so-called Cramerovo rule which allows us to solving systems of linear equations.
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Looking for an optimal aiming point in playing darts
Mareček, Petr ; Rajmic, Pavel (referee) ; Mangová, Marie (advisor)
The thesis deals with recommendation optimal point of dartboard. The first part is theoretical, where is described issue of probability, distribution of variation and significant distribution of variation. At the end of theoretical part is described the Fourier transfrom. The second part of the thesis deals with the design and implementation of web application. The design and implemention of web application uses the theoretical part for assigment optimal point of dartboard.
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