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Semianalytical Computation of Fourier Series Coeficients
Hégr, Tomáš ; Kunovský, Jiří (referee) ; Šátek, Václav (advisor)
This bachelor thesis deals with semianalytical computation of the coefficients of the Fourier series. The aim of this work is to create a graphical user interface for program TKSL/C. The work contains the theory of Fourier series and Fourier transforms. The state of the art software is described in the following chapter. In the next parts the thesis describes the concept of the implementation of the user interface, some tutorial examples which were used and the summary of user testing.
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Electronic Circuits Simulation
Žabka, Michal ; Kocina, Filip (referee) ; Šátek, Václav (advisor)
The aim of this bachelor thesis is to introduce the most popular numerical methods for solving differential equation. Following part describe a electronic circuits and simulation programs. First part of this thesis is focused on the Taylor series method computation and its parallel solution. In another chapters, it will be describe the methods for solution of electronic circuits, the process of designing a model of CMOS inverter, CMOS NAND and CMOS NOR. The final part of this thesis is focused on simulation in various simulation programs and evaluation of the effectiveness of individual methods.
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Finite Integrals Numerical Computations
Mikulka, Jiří ; Šátek, Václav (referee) ; Kunovský, Jiří (advisor)
The application of the finite integral of multiple variable functions is penetrating into more and more industries and science disciplines. The demands placed on solutions to these problems (such as high accuracy or high speed) are often quite contradictory. Therefore, it is not always possible to apply analytical approaches to these problems; numerical methods provide a suitable alternative. However, the ever-growing complexity of these problems places too high a demand on many of these numerical methods, and so neither of these methods are useful for solving such problems. The goal of this thesis is to design and implement a new numerical method that provides highly accurate and very fast computation of finite integrals of multiple variable functions. This new method combines pre-existing approaches in the field of numerical mathematics.
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Performance Engineering of Stencils Optimization in Geometric Multigrid
Janalík, Radim ; Šátek, Václav (referee) ; Kunovský, Jiří (advisor)
V této práci představujeme blokovou metodu pro zlepšení lokality v cache paměti u výpočtů typu stencil a dva nástroje, Pluto a PATUS, které tuto metodu používají ke generování optimalizovaného kódu. Provádíme různá měření a zkoumáme zrychlení výpočtu při použití různých optimalizací. Nakonec implementujeme vyhlazovací krok v multigridu s různými optimalizacemi a zkoumáme jak se tyto optimalizace projeví na výkonu multigridu.
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Hardware Realization of Higher Order Numerical Integrator
Matečný, František ; Veigend, Petr (referee) ; Šátek, Václav (advisor)
This work describes numerical integration and solution for ordinary differential equations by the Taylor series by different types of integrators. The next part is a description of floating point and fixed point arithmetic. Subsequently, we are presenting designs and calculation methods for parallels multiplication and division integrators in floating point and fixed point arithmetic. The designs were realized in VHDL and implemented on FPGA. Finally we summarizes the proposed solution and compare time complexity with another numerical methods.
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Application of Music Therapy in Special Education for i-CT Framework
Bártů, Tomáš ; Šátek, Václav (referee) ; Fiala, Jiří (advisor)
This bachelor thesis describes development of virtual guitar application for the purposes of music therapy in environment of special education for mentally challenged. Hence this thesis deals with issues of development of similarly focused applications, an analysis of some already existing applications of this kind and a design, implementation of a new application. The resulting application follows on design principles of " Computer as Therapy " project and it is based on i-CT Framework simplifying design and development of applications in indicated environment. The development is focused on multi-platform development with support for operating system Android and iOS. The verification of the application has been done in environment of mentally challenged people.
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Stiff Systems Analysis
Šátek, Václav ; Dalík, Josef (referee) ; Horová, Ivana (referee) ; Kunovský, Jiří (advisor)
The solving of stiff systems is still a contemporary sophisticated problem. The basic problem is the absence of precise definition of stiff systems. A question is also how to detect the stiffness in a given system of differential equations. Implicit numerical methods are commonly used for solving stiff systems. The stability domains of these methods are relatively large but the order of them is low. The thesis deals with numerical solution of ordinary differential equations, especially numerical calculations using Taylor series methods. The source of stiffness is analyzed and the possibility how to reduce stiffness in systems of ordinary differential equations (ODEs) is introduced. The possibility of detection stiff systems using explicit Taylor series terms is analyzed. The stability domains of explicit and implicit Taylor series are presented. The solutions of stiff systems using implicit Taylor series method are presented in many examples. The multiple arithmetic must be used in many cases. The new suitable parallel algorithm based on implicit Taylor series method with recurrent calculation of Taylor series terms and Newton iteration method (ITMRN) is proposed.
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Automatic Adjustment of Photographed Documents
Kuchta, Lukáš ; Šátek, Václav (referee) ; Rozman, Jaroslav (advisor)
This work deals with the automatic editing of photographed documents, specifically the creation of a library that will take care of cropping, alignment, transformation and brightness editing of photographed documents. The goal is to use this library to create a program into which a photo of the document is uploaded and which returns a modified version of the document. The functions of the OpenCV library for the Python programming language are used for the implementation of the library, specifically the functions for finding the edges of the document pages, their cropping, alignment and brightness adjustment. The PyQtlibrary is used to create the graphical user interface of the resulting program. The goal was fulfilled, a program with a pleasant user interface for automatic editing of photographed documents was created. The benefit of this work is the possibility of using the created program to detect documents in the image and edit them.
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Automated Exam Generation System
Kapusta, Vlastimil ; Šátek, Václav (referee) ; Barabas, Maroš (advisor)
This bachelor's thesis describes graphic design, used technology and implementation of the automated exam generation system. As the implementation language was chosen Java programming language. This thesis deals with usage of the Swing GUI component library and with using Insubstantial and SwingX libraries which extend the Swing library. Important part of this thesis is connecting Java and document preparation system LaTeX. Result is an application that allows creating exams. It is also possible to store and load unfinished exams and export them into tex or pdf format.
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Effective Algorithms for High-Precision Computation of Elementary Functions
Chaloupka, Jan ; Kunovský, Jiří (referee) ; Šátek, Václav (advisor)
Nowadays high-precision computations are still more desired. Either for simulation on a level of atoms where every digit is important and inaccurary in computation can cause invalid result or numerical approximations in partial differential equations solving where a small deviation causes a result to be useless. The computations are carried over data types with precision of order hundred to thousand digits, or even more. This creates pressure on time complexity of problem solving and so it is essential to find very efficient methods for computation. Every complex physical problem is usually described by a system of equations frequently containing elementary functions like sinus, cosines or exponentials. The aim of the work is to design and implement methods that for a given precision, arbitrary elementary function and a point compute its value in the most efficent way. The core of the work is an application of methods based on AGM (arithmetic-geometric mean) with a time complexity of order $O(M(n)\log_2{n})$ 9(expresed for multiplication $M(n)$). The complexity can not be improved. There are many libraries supporting multi-precision atithmetic, one of which is GMP and is about to be used for efficent method implementation. In the end all implemented methods are compared with existing ones.
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