設H是一個實數正交的矩陣，我們要求它的特徵值以及特徵向量。H可以表示成Schur參數的形式。根據Ammar，Gragg及Reichel的論文，我們把H的特徵問題轉換成兩個元素由Schur參數決定的二對角矩陣的奇異值(奇異向量)的問題。我們用這個方法寫成程式並且與CLAPACK的程式比較準確度及速度。最後列出一些數值的結果作為結論。 / Let H be an orthogonal Hessenberg matrix whose eigenvalues, and possibly eigenvectors, are to be determined. Then H can be represented in Schur parametric form [2]. Following Ammar, Gragg, and Reichel's paper [1], we compute the eigenproblem of H by finding the singular values (and vectors) of two bidiagonal matrices whose elements are explicitly known functions of the Schur parameters. We compare the accuracy and speed of our programs using the method described aboved with those in CLAPACK. Numerical results conclude this thesis.

The analytical solution of a given inhomogeneous boundary value problem of a linear, elliptic, inhomogeneous partial differential equation and a set of inhomogeneous mixed Dirichlet- and Neumann-type boundary conditions is derived in the present paper. In the context of elasticity theory, the problem arises for a non-conservative symmetric ansatz and an extended constitutive law shown earlier. For convenient user application, the scalar function expressed in cylindrical coordinates is primarily obtained for the general case before being expatiated on a special case of linear boundary conditions.

In addition to previous publications, the paper presents the analytical solution of a special boundary value problem which arises in the context of elasticity theory for an extended constitutive law and a non-conservative symmetric ansatz. Besides deriving the general analytical solution, a specific form for linear boundary conditions is given for user convenience.

No description available.

A tese apresenta um método para a solução dos problemas do valor inicial (PVIs) com margens de erro comparáveis às de métodos numéricos consagrados (MN), tanto para a função quanto para suas derivadas. O método é aplicável a equações diferenciais (EDs) lineares ou não, sendo o ferramental desenvolvido até a quarta ordem, que pode ser expandido para ordens superiores. A solução é uma expressão polinomial de alto grau com coeficientes expressos pela razão entre dois inteiros. O método se mostra eficaz mesmo em alguns casos em que os MN não conseguiram dar a partida. As resoluções são obtidas considerando que o espaço de soluções é um espaço de Hilbert, equipado com a base completa dos polinômios de Legendre. Em decorrência do método aqui desenvolvido, os majorantes de erros para a função e derivadas são determinados analiticamente por um cálculo matricial também deduzido nesta tese. Paralelamente a toda fundamentação analítica, foi desenvolvido o software SAM, que automatiza todas as tarefas na busca de soluções dos PVIs. A tese propõe e verifica a validade de um novo critério de erro no qual pesam tanto os erros locais quanto os erros globais, simultaneamente. Como subprodutos dos resultados já descritos, igualmente integrados ao SAM, obtiveram-se também: (1) Um critério objetivo para analisar a qualidade de um MN, sem necessidade do conhecimento de seu algoritmo; (2) Uma ferramenta para aproximações polinomiais de alta precisão para funções de quadrado integrável em determinado intervalo limitado, com um majorante de erro; (3) Um ferramental analítico para transposição genérica (linear ou não) dos PVIs até 4ª ordem, nas mudanças de domínio; (4) As matrizes de integração e diferenciação genéricas para todas as bases polinomiais do espaço de Hilbert. / This thesis shows a new method to get polynomial solutions to the initial value problems (IVP), with an error margin comparable to the consecrate numerical methods (NM), for both the function and its derivatives. The method works with differential equations (DEs) linear or not, beeing the developed tolls available until 4th order, whose can be expanded to higher orders. The solution is a polynomial high degree expression with coefficients expressed by the ratio between two integers. The method behaves efficiently even in some cases that NM cannot get started. The resolutions are gotten considering that, the solution space is a Hilbert space, equipped with a complete set basis of Legendre Polynomials. Due the method here developed, the errors majoratives for the function and its derivatives are found analytically by a matrix calculus, also derived in this thesis. Beside all analytical foundation, a software (SAM) was developed to automate the whole process, joining all the tasks involved in the search for solutions to the IVP. This thesis proposes, verifies and validates a new error criterion, which takes in account simultaneously the local and global errors. As sub-products of the results described before, also integrated to the SAM, the following achievements should be highlighted: (1) An objective criterion to analyze the quality of any NM, despite of the knowledge of its algorithm; (2) A tool for a polynomial approximation, of high precision, for functions whose square is integrable in a given limited domain, with an errors majorative; (3) A tool-kit for a generically transpose (linear or not) of the IVPs domain and form, taking into account its derivatives, until the 4th order; (4) The generic matrices for integration and differentiation for all the polynomial basis of the Hilbert space.

Made available in DSpace on 2015-03-03T15:32:43Z (GMT). No. of bitstreams: 1 MarcioLN_DISSERT.pdf: 2785073 bytes, checksum: 8f894388b11b263c73e967b4b680c52f (MD5) Previous issue date: 2013-08-13 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / This paper has two objectives: (i) conducting a literature search on the criteria of uniqueness of solution for initial value problems of ordinary differential equations. (ii) a modification of the method of Euler that seems to be able to converge to a solution of the problem, if the solution is not unique / O presente trabalho tem dois objetivos: (i) a realiza??o de uma pesquisa bibliografifica sobre os crit?rios de unicidade de solu??o para problemas de valor inicial de equa??es diferenciais ordin?rias. (ii) Introduzir uma modifica??o do m?todo de Euler que parece ser capaz de convergir a uma das solu??es do problema, caso a solu??o n?o seja ?nica

This thesis consists of three self-contained parts, each with its own abstract, body, references and page numbering. Part I, 'Potential theory, path integrals and the Laplacian of the indicator', finds the transition density of absorbed or reflected Brownian motion in a d-dimensional domain as a Feynman-Kac functional involving the Laplacian of the indicator, thereby relating the hitherto unrelated fields of classical potential theory and path integrals. Part II, 'The problem of alternatives', considers parallel investment in alternative technologies or drugs developed over time, where there can be only one winner. Parallel investment accelerates the search for the winner, and increases the winner's expected performance, but is also costly. To determine which candidates show sufficient performance and/or promise, we find an integral equation for the boundary of the optimal continuation region. Part III, 'Optimal support for renewable deployment', considers the role of government subsidies for renewable technologies. Rapidly diminishing subsidies are cheaper for taxpayers, but could prematurely kill otherwise successful technologies. By contrast, high subsidies are not only expensive but can also prop up uneconomical technologies. To analyse this trade-off we present a new model for technology learning that makes capacity expansion endogenous. There are two reasons for this standalone structure. First, the target readership is divergent. Part I concerns mathematical physics, Part II operations research, and Part III policy. Readers interested in specific parts can thus read these in isolation. Those interested in the thesis as a whole may prefer to read the three introductions first. Second, the separate parts are only partially interconnected. Each uses some theory from the preceding part, but not all of it; e.g. Part II uses only a subset of the theory from Part I. The quickest route to Part III is therefore not through the entirety of the preceding parts. Furthermore, those instances where results from previous parts are used are clearly indicated.

No description available.

One of the main problems of current physical geodesy is the unification of local height systems and the creation of the unified global vertical reference frame, whose primary definition constant will be the geopotential value of W0 on the level surface, such as geoid. This problem encounters several pitfalls, such as different types of physical heights used in the world, ways of eliminating the effects of tides on the shape of the Earth's body. The first parts of the thesis describe the theoretical foundations concerning the description of the Earth's gravitational field, the basics of height theory and the solution of the boundary value problems used in geodesy, together with the solution of the Hotine's and Stokes' integral by convolution. Due to the fact that the data of directly measured gravity acceleration for the territory of the Czechia and the Slovakia are not freely available with sufficient coverage, these data were replaced by gravity disturbances calculated from the Global Gravity Model of the Earth. To improve the data obtained from geopotential models, so-called residual terrain modelling was used. It is a spectral combination of gravity field models with relevant Earth's gravitational field quantities, which are obtained by modeling from a digital terrain model and a height model that represents the mean value of topography. The combination of these data consists of calculating those frequencies of the gravitational signal from the digital terrain model that are not a part of the signal obtained from geopotential models that in general have a lower spatial resolution. Two methods were used to connect the local height systems of the Czechia and the Slovakia. The first method was to use the solution of Molodensky's problem. The second method used is originally a method developed to test geopotential models. Both methods were tested on a set of measuring points (GNSS/levelling points).

Thesis deals with solving the problems of continuum mechanics by method of Isogeometric analysis. This relatively young method combines the advantages of precise NURBS geometry and robustness of the classical finite element method. The method is described on procedure of solving a plane Poissons boundary value problem. Solver is implemented in MatLab and algorithms are attached to the text.