National Repository of Grey Literature 75 records found  1 - 10nextend  jump to record: Search took 0.01 seconds. 
Numerical comparison of the CGLS and LSQR algorithms
Mrňák, Petr ; Tichý, Petr (advisor) ; Tůma, Miroslav (referee)
This bachelor thesis deals with the introduction of two mathemati- cally equivalent algorithms, CGLS and LSQR, which can be viewed as versions of the method of conjugate gradients applied to a system of normal equations. This thesis is devoted to their comparison both from a theoretical point of view (showing the relations between vectors and coefficients) and from a practical point of view (the behaviour of both algorithms in finite precision arithmetic). 1
Numerical comparison of the CGLS and LSQR algorithms
Mrňák, Petr ; Tichý, Petr (advisor) ; Tůma, Miroslav (referee)
This bachelor thesis deals with the introduction of two algorithms, namely LSQR and CGLS, and then their comparison in the field of theory and the field of practi- cal application and computation. First, it is important to lay the foundations for these algorithms by using conjugate gradients and Lanczos tridiagonalisation. Both algorithms are theoretically equivalent, but in practice it is necessary to distinguish between them which is more appropriate for a given calculation. 1
Computations of Google's PageRank
Smejkalová, Barbora ; Tichý, Petr (advisor) ; Tůma, Miroslav (referee)
The thesis is concerned with numerical methods for solving the PageRank problem. The PageRank problem is formulated and mathematically described, based on intuitive observations called theses. We introduce and analyze two nu- merical methods for solving the resulting algebraic problems, namely the power method and the inner-outer method. The presented numerical experiments demonstrate and compare the behavior of the methods for various test matrices and input parameters. 1
Efficient methods for visualization of volumetric data
Holeček, Martin ; Hron, Jaroslav (advisor) ; Tůma, Miroslav (referee)
Title: Efficient methods for visualization of volumetric data Author: Martin Holeček Department: Mathematical Institute of Charles University Supervisor: RNDr. Ing. Jaroslav Hron, Ph.D., Mathematical Institute Abstract: The aim is to make an overview of and present implementation usefull for rendering of simulated datasets and CT and MR datasets. We will examine the methods of direct volume rendering of structured and unstructured grids and head to meaningful simultaneous realtime rendering of both types. In the first part, we briefly present the development, problems and targets of the field. Next, based on knowledge about existing algorithms, we choose one solution and present our own implementation and modification of algorithms. In detail, the object of our study will be numerical solutions of volume rendering integral by preintegration and paralelization of the process of projecting tetrahedra and perspective correction. For practical reasons we focus on the efficiency, that means computation time, used memory and usefullnes for medical presentation. The results will be compared with some other existing implementations. Keywords: volume rendering, preintegration, unstructured grid
Incomplete Cholesky factorization
Hoang, Phuong Thao ; Tůma, Miroslav (advisor) ; Tichý, Petr (referee)
The thesis is about the incomplete Cholesky factorization and its va- riants, which are important for preconditioning a system with symmetric and positive definite matrix. Our main focus is on solving these systems, which arise in many technical applications and natural sciences, using preconditioned Con- jugate Gradients. Besides many other ways we can apply Cholesky factorization approximately, incompletely. In this thesis we study existence of the incomplete Cholesky factorization and we evaluate behaviour and potential of different vari- ants of the generic algorithm. 1
Transformace Sylvestrovy matice a výpočet největšího společného dělitele dvou polynomů
Eckstein, Jiří ; Zítko, Jan (advisor) ; Tůma, Miroslav (referee)
In this thesis we study the computation of the greatest common divisor of two polynomials. Firstly, properties of Sylvester matrices are considered as well as their role in computation. We then note, that this approach can be naturally generalized for several polynomials. In the penultimate section, Bézout matrices are studied as an analogy to the Sylvester ones, providing necessary comparison. Extension for more than polynomials is presented here as well. Algorithms corresponding to the individual approaches are presented as well. Finally, the algorithms are implemented in MATLAB and are compared in numerical experiments. Powered by TCPDF (www.tcpdf.org)
Matrix-free preconditioning
Trojek, Lukáš ; Duintjer Tebbens, Erik Jurjen (advisor) ; Tůma, Miroslav (referee)
The diploma theses is focused on matrix-free preconditioning of a linear system. It gives a very brief introduction into the area of iterative methods, preconditioning and matrix-free environment. The emphasis is put on a detailed description of a variant of LU factorization which can be computed in a matrix-free manner and on a new technique connected with this factorization for preconditioning by incomplete LU factors in matrix-free environment. Its main features are storage of only one of the two incomplete factors and low memory costs during the computation of the stored factor. The thesis closes with numerical experiments demonstrating the efficiency of the proposed technique.
Low-rank matrix approximations
Jarolímová, Alena ; Tůma, Miroslav (advisor) ; Vlasák, Miloslav (referee)
This thesis is focused on using low rank matrices in numerical mathematics. We introduce conjugate gradient method and its preconditioning which we use in other chapters. Then we describe four different approaches to approximation using low rank matrices. First we discuss classical approximation using singu- lar value decomposition. Next, using a model problem, we describe hierarchical matrices, which are connected with applications in physics and technique. Then pseudo-skeleton decomposition is introduced. We formulate and prove a theorem about error estimate of this decomposition. We also mention algorithm Maxvol which can compute pseudo-skeletal decomposition of tall matrices. Next chapter is dedicated to probabilistic algorithms and to least-squares solver Blendenpik. In conclusions we show results of experiments focused on preconditioning using algorithm Maxvol. 1
Field of values of a matrix: Theory and computation
Vacek, Lukáš ; Tichý, Petr (advisor) ; Tůma, Miroslav (referee)
The field of values of a matrix A is a convex set in the complex plane assigned to A. It is important in matrix analysis, especially in invetigation of properties of nonnormal matrices and matrix polynomials, in study of the con- vergence of iterative methods applied to these matrices, in the estimation of ma- trix function norms, etc. This thesis summarizes theory about the field of values of a matrix, formulates open problems and explaines the main idea of the basic numerical method for its computation. In numerical experiments the standart algorithmic realization of method is compared with alternative approaches that use power method, Lanczos algorithm and Chebfun.

National Repository of Grey Literature : 75 records found   1 - 10nextend  jump to record:
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