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Approximating stable densities with Padé approximants and asymptotic seriesLiang, Jiaxi January 2011 (has links)
In this thesis, we are interested in using the Padé approximants and asymptotic series to approximate the density functions of the stable distributions. The paper specifically discusses the selection of the optimal degree and central point of Padé approximants as well as how to connect the Padé approximants and asymptotic series as a piecewise function. Based on such approximation, a computational algorithm is developed to estimate the maximum likelihood estimator with confidence interval of the parameters, using quasi-Newton method. Simulations are conducted to evaluate the performance of this algorithm, and comparisons are made to Nolan's integral method to show that the method introduced in the thesis is fast and reliable in approximation and estimation.
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Approximating stable densities with Padé approximants and asymptotic seriesLiang, Jiaxi January 2011 (has links)
In this thesis, we are interested in using the Padé approximants and asymptotic series to approximate the density functions of the stable distributions. The paper specifically discusses the selection of the optimal degree and central point of Padé approximants as well as how to connect the Padé approximants and asymptotic series as a piecewise function. Based on such approximation, a computational algorithm is developed to estimate the maximum likelihood estimator with confidence interval of the parameters, using quasi-Newton method. Simulations are conducted to evaluate the performance of this algorithm, and comparisons are made to Nolan's integral method to show that the method introduced in the thesis is fast and reliable in approximation and estimation.
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Orthogonal Polynomials on S-Curves Associated with Genus One SurfacesBarhoumi, Ahmad 08 1900 (has links)
Indiana University-Purdue University Indianapolis (IUPUI) / We consider orthogonal polynomials P_n satisfying orthogonality relations where the measure of orthogonality is, in general, a complex-valued Borel measure supported on subsets of the complex plane. In our consideration we will focus on measures of the form d\mu(z) = \rho(z) dz where the function \rho may depend on other auxiliary parameters. Much of the asymptotic analysis is done via the Riemann-Hilbert problem and the Deift-Zhou nonlinear steepest descent method, and relies heavily on notions from logarithmic potential theory.
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Percolação direcionada em redes regulares bidimensionais. / Directed percolation on two-dimensional regular lattices.Neves, Ubiraci Pereira da Costa 24 April 1992 (has links)
Utilizando uma técnica de matriz de transferência, expandimos em série a probabilidade de percolação P(q) para o problema da percolação por sítio na rede quadrada direcionada. Nosso método revela uma inesperada conexão entre este problema e o da enumeração dos modos de se dissecar uma bola. Mostramos que o método pode também ser usado para se expandir em série o tamanho médio do cluster S (p) . Uma análise baseada nos aproximantes de Padé fornece estimativas do valor crítico pc, e também do expoente crítico β. / Using a transfer matrix technique we obtain an extended series expansion of the percolation probability P(q) for the directed site percolation problem on the square lattice. Our method reveals an up to now unsuspected connection between this problem and the enumeration of the ways of dissecting a ball. We show that the method can also be used to determine a series expansion for the mean cluster size S(p). An analysis based on Padé approximants gives estimates of the critical threshold pc, and also of the critical exponent β.
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Percolação direcionada em redes regulares bidimensionais. / Directed percolation on two-dimensional regular lattices.Ubiraci Pereira da Costa Neves 24 April 1992 (has links)
Utilizando uma técnica de matriz de transferência, expandimos em série a probabilidade de percolação P(q) para o problema da percolação por sítio na rede quadrada direcionada. Nosso método revela uma inesperada conexão entre este problema e o da enumeração dos modos de se dissecar uma bola. Mostramos que o método pode também ser usado para se expandir em série o tamanho médio do cluster S (p) . Uma análise baseada nos aproximantes de Padé fornece estimativas do valor crítico pc, e também do expoente crítico β. / Using a transfer matrix technique we obtain an extended series expansion of the percolation probability P(q) for the directed site percolation problem on the square lattice. Our method reveals an up to now unsuspected connection between this problem and the enumeration of the ways of dissecting a ball. We show that the method can also be used to determine a series expansion for the mean cluster size S(p). An analysis based on Padé approximants gives estimates of the critical threshold pc, and also of the critical exponent β.
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Frações contínuas que correspondem a séries de potências em dois pontosLima, Manuella Aparecida Felix de [UNESP] 19 February 2010 (has links) (PDF)
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lima_maf_me_sjrp.pdf: 528569 bytes, checksum: 3cad2d8f7175d945b2ead7fb45a5c4e1 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / O principal objetivo deste trabalho é estudar métodos para construir os numeradores e denominadores parciais da fração contínua que corresponde a duas expansões em série de potências de uma função analítica f(z); em z =0 e em z = 00. / The main purpose of this work is to two series expansions of an analytic function f(z); in z =0 and z =00 simultaneously. Furthermore we considered the case when there are zero coefficients in the series and also whwn there is symmetry in the coefficients of the two series. Some examples are given.
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ORTHOGONAL POLYNOMIALS ON S-CURVES ASSOCIATED WITH GENUS ONE SURFACESAhmad Bassam Barhoumi (8964155) 16 June 2020 (has links)
We consider orthogonal polynomials P_n satisfying orthogonality relations where the measure of orthogonality is, in general, a complex-valued Borel measure supported on subsets of the complex plane. In our consideration we will focus on measures of the form d\mu(z) = \rho(z) dz where the function \rho may depend on other auxiliary parameters. Much of the asymptotic analysis is done via the Riemann-Hilbert problem and the Deift-Zhou nonlinear steepest descent method, and relies heavily on notions from logarithmic potential theory.
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Uso de aproximantes de Padé na estimação de parâmetros modais em estruturas de grande porte. / Use of Padé approximants for modal parameters estimation on large scale structures.Luiz Antonio Barbosa Coelho 18 December 2008 (has links)
Este trabalho apresenta um novo algoritmo para a estimação de frequências e amortecimentos de vibrações, baseado em aproximantes de Padé, a partir da análise de sinais temporais oriundos de estruturas de grande porte. O algoritmo se baseia nas propriedades de convergência dos aproximantes de Padé, que garantem a existência de pólos que representam corretamente as componentes senoidais do sinal, e numa peculiar distribuição de pólos e zeros espúrios que decorrem da sobre-determinação do aproximante. O comportamento estatístico do algoritmo é estudado através de experimentos numéricos e sua aplicação em um caso real é feita. / This work introduces a novel estimation technique for vibration frequency and damping estimation, based on Padé approximants, and using time series taken from large structures. The algorithm is based on convergence properties of Padé approximants that assures the existence of real poles representing the sinusoidal components of the signal, and a remarkable distribution of stray poles and zeros, resulting from the approximant overdetermination. Its statistical behavior is analyzed through numerical experiments and an application for a real structure is provided as example.
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Uso de aproximantes de Padé na estimação de parâmetros modais em estruturas de grande porte. / Use of Padé approximants for modal parameters estimation on large scale structures.Coelho, Luiz Antonio Barbosa 18 December 2008 (has links)
Este trabalho apresenta um novo algoritmo para a estimação de frequências e amortecimentos de vibrações, baseado em aproximantes de Padé, a partir da análise de sinais temporais oriundos de estruturas de grande porte. O algoritmo se baseia nas propriedades de convergência dos aproximantes de Padé, que garantem a existência de pólos que representam corretamente as componentes senoidais do sinal, e numa peculiar distribuição de pólos e zeros espúrios que decorrem da sobre-determinação do aproximante. O comportamento estatístico do algoritmo é estudado através de experimentos numéricos e sua aplicação em um caso real é feita. / This work introduces a novel estimation technique for vibration frequency and damping estimation, based on Padé approximants, and using time series taken from large structures. The algorithm is based on convergence properties of Padé approximants that assures the existence of real poles representing the sinusoidal components of the signal, and a remarkable distribution of stray poles and zeros, resulting from the approximant overdetermination. Its statistical behavior is analyzed through numerical experiments and an application for a real structure is provided as example.
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Frações contínuas que correspondem a séries de potências em dois pontos /Lima, Manuella Aparecida Felix de. January 2010 (has links)
Orientador: Eliana Xavier Linhares de Andrade / Banca: Vanessa Avansini Botta Pirani / Banca: Cleonice Fátima Bracciali / Resumo: O principal objetivo deste trabalho é estudar métodos para construir os numeradores e denominadores parciais da fração contínua que corresponde a duas expansões em série de potências de uma função analítica f(z); em z =0 e em z = 00. / Abstract: The main purpose of this work is to two series expansions of an analytic function f(z); in z =0 and z =00 simultaneously. Furthermore we considered the case when there are zero coefficients in the series and also whwn there is symmetry in the coefficients of the two series. Some examples are given. / Mestre
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