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1
Brookes, Richard G. "The quadratic Hermite-Padé approximation." Thesis, University of Canterbury. Mathematics, 1989. http://hdl.handle.net/10092/8886.
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This thesis is concerned with the existence, behaviour and performance of the quadratic Hermite-Padé approximation.
It starts with the definition of the general Hermite-Padé approximation. Some of the problems which arise, particularly those of finding Hermite-Padé forms and the existence of approximations are discussed. Chapter 3 solves the existence problem in the quadratic case whilst Chapter 2 presents a recurrence algorithm for finding quadratic forms which can easily be extended to general Hermite-Padé forms.
Chapters 4 and 5 compare the performance of the quadratic, Padé and Taylor approximations using particular examples over a variety of regions. Many graphs and contour maps of the various approximations and error functions are given. The quadratic approximation is shown to be superior in these cases.
Finally, in Chapter 6, a theorem concerning sequences of quadratic approximations is presented and the structure of the quadratic table is explored.
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Khémira, Samy. "Approximants de Hermite-Padé, déterminants d'interpolation et approximation diophantienne." Phd thesis, Université Pierre et Marie Curie - Paris VI, 2005. http://tel.archives-ouvertes.fr/tel-00009653.
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Cette thèse aborde des sujets d'approximation diophantienne et de transcendance liés aux fonctions exponentielles. Il est tout d'abord établit des liens entre les coefficients d'approximants de Hermite-Padé, ceux de polynômes d'interpolation de Hermite et certains cofacteurs d'un déterminant de Vandermonde généralisé. Nous utilisons ensuite la notion de hauteur d'une matrice (que nous majorons grâce aux liens précédemment fournis) afin de donner une nouvelle démonstration de la transcendance de $e$. Ces résultats nous permettent finalement d'obtenir de nouveaux énoncés d'approximation diophantienne tels que la minoration de la distance de l'exponentielle d'un nombre algébrique (de hauteur absolue logarithmique de Weil bornée) à un autre nombre algébrique (lui aussi de hauteur absolue logarithmique de Weil bornée) en fonction de ces mêmes bornes. Il est ensuite donné, pour différentes valeurs de nombres rationnels $a$, quelques estimations remarquables telles que le minimum, sur l'ensemble des entiers non nuls $b$ et $c$, de la distance $|e^(b)-a^(c)|$.
3
Dujardin, Bénédicte. "Approximation rationnelle appliquée au traitement de données." Nice, 2005. http://www.theses.fr/2005NICE4106.
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Nous abordons dans ce document divers problèmes relevant des mathématiques et du traitement de données dont le point commun est de faire intervenir des polynômes à coefficients aléatoires, dont l’étude compose exclusivement la matière du premier chapitre. En analyse spectrale, l’utilisation de modèles paramétriques linéaires d’un signal conduit à des estimateurs rationnels de sa densité spectrale de puissance. Nous nous intéressons aux estimateurs AR et ARMA de certains processus stochastiques et caractérisons leurs performances en terme de statistique de leurs pôles et zéros complexes. Notre compréhension du rôle tenu par la composante aléatoire du signal est facilitée par une partie préliminaire consacrée aux approximants rationnels de Padé de séries formelles perturbées aléatoirement. Cette première partie est pour nous l’occasion de mettre en évidence certains problèmes récurrents liés à la perturbation tels que l’appariement des pôles et des zéros ou la formation de structures cristallinesIn this document, we are concerned with different problems arising from mathematics and date processing whose common point is to involve polynomials with random coefficients, the study of which composes exclusively the material of the first chapter. In spectral analysis, the use of linear parametric models of a signal leads to rational estimators of its power spectrum density. We are interested in the AR and ARMA estimators of certain stochastic processes and characterize their performance in terms of the statistics of their complex poles and zeros. Our understanding of the role played by the random component of the signal is made easier by a preliminary part devoted to rational Padé approximants of randomly perturbed formal series. This first part provides us with the opportunity to underline some recurring phenomena related to the perturbation such as the matching of poles and zeros or the formation of crystal structures
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RIBEIRO, LUIZ CLAUDIO. "IDENTIFICATION OF BOX AND JENKINS: A COPARISON BETWEEN FACE AND PADÉ APPROXIMATION." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 1992. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=9016@1.
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Desde de 1970, quando Box e Jenkins introduziram os
modelos ARMA para análise e previsão de séries
temporais,
muitos estudos foram desenvolvidos buscando encontrar um
método mais eficiente de identificação de tais modelos.
Tal fato se deu porque o método por Box e Jenkins,
baseado
na função de auto-correlação parcial (FACP) não são
eficientes quando os modelos apresentam componentes auto-
regressivas (AR) e médias móveis (MA).
Estudos comparativos realizados anteriormente mostraram
que dentre os métodos de identificação já desenvolvidos,
o
que se mostrou mais eficiente foi o baseado na função de
auto-correlação extendida (FACE) de TIAO e TSAY (1992)
Recentemente, Kuldeep Kumar introduziu na literatura um
método de identificação baseado na teoria de aproximação
de Padé. O objetivo deste trabalho é comparar o método
da
FACE com o método baseado na teoria de aproximação de
Padé.Since 1970, when Box and Jenkins first introduced the ARMA models to analysis and predict of time series data, a lot of studies have been developed to find an efficient identification method for such models. This was due the fact that the identification method proposed by Box and Jenkins, based on Auto-correlation Function (ACF) and Partial Auto-correlation Function (PACF), are inefficient when the models have auto regressive - AR- and moving average - MA- components. Comparative studies undertaken, have shown that, among the identification methods already developed, the method based on the Extended Auto-correlation Fuction of Tiao and Tsay (1982) is the most efficient. More recently, however, Kuldeep Kumar has introduced in the literature an identification method based on the theory of Padé aproximation. The objective of this paper is to compare the Extended Auto-correlation Function method with the method based on the Theory of Padé approximation.
5
Heimonen, A. (Ari). "On effective irrationality measures for some values of certain hypergeometric functions." Doctoral thesis, University of Oulu, 1997. http://urn.fi/urn:isbn:9514247191.
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Abstract
The dissertation consists of three articles in which irrationality measures for some values of certain special cases of the Gauss hypergeometric function are considered in both archimedean and non-archimedean metrics.
The first presents a general result and a divisibility criterion for certain products of binomial coefficients upon which the sharpenings of the general result in special cases rely. The paper also provides an improvement concerning th e values of the logarithmic function. The second paper includes two other special cases, the first of which gives irrationality measures for some values of the arctan function, for example, and the second concerns values of the binomial function. All the results of the first two papers are effective, but no computation of the constants for explicit presentation is carried out. This task is fulfilled in the third article for logarithmic and binomial cases. The results of the latter case are applied to some Diophantine equations.
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Fontgalland, Glauco. "Contribution à l'étude des procédés d'accélération de convergence dans la méthode des éléments de frontière." Toulouse, INPT, 1999. http://www.theses.fr/1999INPT014H.
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Dans ce travail, l'analyse rigoureuse des discontinuités en guides d'ondes de différentes natures est présentée. Dans ce contexte, les modes des guides à nervures obtenus à l'aide de la méthode des éléments de frontières (BEM) sont utilisés dans la caractérisation des structures guidantes. Cette analyse est précédée de l'étude qualitative des méthodes intégrales pour la résolution des problèmes homogènes dans les guides d'ondes à nervures, tels que la méthode des moindres carrés et la méthode du déterminant. La caractéristique non monotone de l'opérateur des modes TE est vérifiée et des études de convergence sur les troncatures des séries sont présentées. Couplée à la méthode récursive, la formation scalaire et vectorielle de la fonction de Green a permis d'alléger et d'accélérer les calculs des modes dans les guides. Les approximants de Pade et les fonctions d'essai de deuxième ordre sont introduits dans l'approche générale en vue d'accélérer la convergence. Une méthode d'optimisation est proposée pour assurer la convergence des solutions en temps réduit. La détermination du potentiel et du champ électromagnétique sur la surface de discontinuité a été présentée. En effet, la connaissance du champ permet d'une part de valider la convergence des solutions et d'autre de valider les conditions aux limites préalablement fixées. Enfin, le calcul d'une discontinuité est réalisé par l'analyse modale des guides en utilisant une formulation variationnelle. Cette analyse est ensuite appliquée à l'étude de composantes en guides d'ondes.
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Rivoal, Tanguy. "Propriétés diophantiennes de la fonction zêta de Riemann aux entiers impairs." Phd thesis, Université de Caen, 2001. http://tel.archives-ouvertes.fr/tel-00004519.
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Cette thèse est consacrée à l'étude des valeurs de la fonction zêta de Riemann aux entiers impairs. Quatre résultats sont démontrés : - Soit $a$ un nombre rationnel, $\vert a \vert <1$. Le Q-espace vectoriel engendré par $1, Li_1(a), Li_2(a),...$ est de dimension infinie. - Le Q-espace vectoriel engendré par $1, \zeta(3), \zeta(5), \zeta(7),...$ est de dimension infinie. - Il existe un entier impair $j$, $5\le j \le 169$ tel que $1, \zeta(3), \zeta(j)$ sont linéairement indépendants sur Q. - Au moins un des neuf nombres $\zeta(5), \zeta(7),..., \zeta(21)$ est irrationnel.
8
Leinonen, M. (Marko). "On various irrationality measures." Doctoral thesis, Oulun yliopisto, 2017. http://urn.fi/urn:isbn:9789526217031.
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Abstract This dissertation consists of four articles on irrationality measures. In the first paper we derive explicit irrationality measures by using the simple continued fraction expansions in a completely new way. In the second and third articles we use Padé approximations to construct irrationality measures. In the second paper we obtain an explicit irrationality measure for the values of q-exponential series, for which the earlier corresponding results are not as explicit. Furthermore, we construct a restricted irrationality measure for the values of q-exponential series, which is an improvement on the earlier results in the restricted case. In the third article we derive the best possible asymptotic restricted irrationality exponent for the values of Jacobi's triple product. In the last paper we consider Cantor series. We generalize the earlier results by deriving Sondow's irrationality measure for some Cantor seriesTiivistelmä Tämä väitöskirja koostuu neljästä artikkelista, jotka kaikki käsittelevät irrationaalisuusmittoja. Ensimmäisessä artikkelissa irrationaalisuusmittoja johdetaan uudella tavalla irrationaalilukujen yksinkertaisista ketjumurtolukuesityksistä. Toisessa ja kolmannessa artikkelissa irrationaalisuusmitat konstruoidaan Padé-approksimaatioiden avulla. Toisessa artikkelissa saadaan eksplisiittinen irrationaalisuusmitta q-eksponenttisarjan arvoille, joiden vastaavat aikaisemmat irrationaalisuusmitat eivät ole näin eksplisiittisiä. Lisäksi samassa artikkelissa konstruoidaan q-eksponenttisarjan arvoille rajoitettu eksplisiittinen irrationaalisuusmitta, mikä parantaa aikaisempia tuloksia rajoitetussa tapauksessa. Kolmannessa artikkelissa johdetaan paras mahdollinen asymptoottinen irrationaalisuuseksponentti Jacobin kolmitulon arvoille. Viimeisessä artikkelissa käsitellään Cantorin sarjoja. Siinä yleistetään aikaisempia tuloksia johtamalla Sondowin irrationaalisuusmitta tietylle joukolle Cantorin sarjoja
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Seppälä, L. (Louna). "Diophantine perspectives to the exponential function and Euler’s factorial series." Doctoral thesis, University of Oulu, 2019. http://urn.fi/urn:isbn:9789529418237.
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Abstract
The focus of this thesis is on two functions: the exponential function and Euler’s factorial series. By constructing explicit Padé approximations, we are able to improve lower bounds for linear forms in the values of these functions. In particular, the dependence on the height of the coefficients of the linear form will be sharpened in the lower bound.
The first chapter contains some necessary definitions and auxiliary results needed in later chapters.We give precise definitions for a transcendence measure and Padé approximations of the second type. Siegel’s lemma will be introduced as a fundamental tool in Diophantine approximation. A brief excursion to exterior algebras shows how they can be used to prove determinant expansion formulas. The reader will also be familiarised with valuations of number fields.
In Chapter 2, a new transcendence measure for e is proved using type II Hermite-Padé approximations to the exponential function. An improvement to the previous transcendence measures is achieved by estimating the common factors of the coefficients of the auxiliary polynomials.
The exponential function is the underlying topic of the third chapter as well. Now we study the common factors of the maximal minors of some large block matrices that appear when constructing Padé-type approximations to the exponential function. The factorisation of these minors is of interest both because of Bombieri and Vaaler’s improved version of Siegel’s lemma and because they are connected to finding explicit expressions for the approximation polynomials. In the beginning of Chapter 3, two general theorems concerning factors of Vandermonde-type block determinants are proved.
In the final chapter, we concentrate on Euler’s factorial series which has a positive radius of convergence in p-adic fields. We establish some non-vanishing results for a linear form in the values of Euler’s series at algebraic integer points. A lower bound for this linear form is derived as well.
10
Jay, Emmanuelle. "Détection en Environnement non Gaussien." Phd thesis, Université de Cergy Pontoise, 2002. http://tel.archives-ouvertes.fr/tel-00174276.
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Les échos radar provenant des diverses réflexions du signal émis sur les éléments de l'environnement (le fouillis) ont longtemps été modélisés par des vecteurs Gaussiens. La procédure optimale de détection se résumait alors en la mise en oeuvre du filtre adapté classique.Avec l'évolution technologique des systèmes radar, la nature réelle du fouillis s'est révélée ne plus être Gaussienne. Bien que l'optimalité du filtre adapté soit mise en défaut dans pareils cas, des techniques TFAC (Taux de Fausses Alarmes Constant) ont été proposées pour ce détecteur, dans le but d'adapter la valeur du seuil de détection aux multiples variations locales du fouillis. Malgré leur diversité, ces techniques se sont avérées n'être ni robustes ni optimales dans ces situations.
A partir de la modélisation du fouillis par des processus complexes non-Gaussiens, tels les SIRP (Spherically Invariant Random Process), des structures optimales de détection cohérente ont pu être déterminées. Ces modèles englobent de nombreuses lois non-Gaussiennes, comme la K-distribution ou la loi de Weibull, et sont reconnus dans la littérature pour modéliser de manière pertinente de nombreuses situations expérimentales. Dans le but d'identifier la loi de leur composante caractéristique qu'est la texture, sans a priori statistique sur le modèle, nous proposons, dans cette thèse, d'aborder le problème par une approche bayésienne.
Deux nouvelles méthodes d'estimation de la loi de la texture en découlent : la première est une méthode paramétrique, basée sur une approximation de Padé de la fonction génératrice de moments, et la seconde résulte d'une estimation Monte Carlo. Ces estimations sont réalisées sur des données de fouillis de référence et donnent lieu à deux nouvelles stratégies de détection optimales, respectivement nommées PEOD (Padé Estimated Optimum Detector) et BORD (Bayesian Optimum Radar Detector). L'expression asymptotique du BORD (convergence en loi), appelée le "BORD Asymptotique", est établie ainsi que sa loi. Ce dernier résultat permet d'accéder aux performances théoriques optimales du BORD Asymptotique qui s'appliquent également au BORD dans le cas où la matrice de corrélation des données est non singulière.
Les performances de détection du BORD et du BORD Asymptotique sont évaluées sur des données expérimentales de fouillis de sol. Les résultats obtenus valident aussi bien la pertinence du modèle SIRP pour le fouillis que l'optimalité et la capacité d'adaptation du BORD à tout type d'environnement.
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Koucha, Yacine. "Approximations to ruin probablities in infinite time using a Lévy process." Master's thesis, Instituto Superior de Economia e Gestão, 2016. http://hdl.handle.net/10400.5/12837.
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Mestrado em Ciências ActuariaisEsta dissertação aborda especificamente problemas da área da teoria da ruína, sub-área da teoria do risco para a atividade seguradora. Em particular, estudamos a probabilidade de ruína eventual. Adaptamos o modelo de risco coletivo de Cramér-Lundberg, estendendo para o modelo perturbado. Adicionamos ao modelo de Poisson composto uma componente representativa de um processo de Lévy (alfa estável). Esta componente adicional permite-nos incorporar incertezas decorrentes de, por exemplo, flutuações de taxas de juro, alterações no número de apólices na carteira, em quaisquer dos casos mantendo as hipóteses tradicionais. Com o objetivo de cálculo da probabilidade de ruína no modelo perturbado, apresentamos novas técnicas, recuperando e generalizando modelos de aproximação bem conhecidos, tais como os de DE VYLDER (1996), DUFRESNE AND GERBER (1989), POLLACZEK-KHINCHINE, PADÉ (ver AVRAM ET AL. (2001) e JOHNSON AND TAAFFE (1989)), obtidas ajustando um, dois, três ou quatro momentos ordinários da distribuição dos montantes das indemnizações. Para além disso, considerámos também importante que as aproximações ajustassem a transformada de Laplace (para a probabilidade de ruína), veja-se FURRER (1998). Avaliamos a qualidade das aproximações estudadas exemplificando para um conjunto de distribuições de cauda leve e de cauda pesada. Ilustramos com detalhe com alguns resultados numéricos.
In this thesis, we work with prominence to a key area in actuarial science, namely ruin theory. The Cramér-Lundberg model of collective risk theory is adapted for the perturbed model, by adding a Lévy (α-stabled) process to the compound Poisson process, which allows us to consider uncertainty to the premium income, fluctuations of the interest rates, changes to the number of policyholders, without neglecting all other assumptions. On the way, we present new approximation techniques, built for the perturbed model in infinite time, and recall a remarkable family of well-known approximations by DE VYLDER (1996), DUFRESNE AND GERBER (1989), POLLACZEK-KHINCHINE and PADÉ (see AVRAM ET. AL (2001) and JOHNSON AND TAAFFE (1989)), obtained by fitting one, two, three or four (we also attempt five) ordinary moments of the claim amount distribution, and thus significantly generalising these approximations. Finding such approximation which fit the Laplace transform of the ruin probability would also be quite valuable, see FURRER (1998). We test the accuracy of the approximations using a mixture of light and heavy tailed distributions for the individual claim amount. We evaluate the ultimate ruin probability and illustrate in detail some numerical results.
N/A
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Neiger, Vincent. "Bases of relations in one or several variables : fast algorithms and applications." Thesis, Lyon, 2016. http://www.theses.fr/2016LYSEN052.
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Dans cette thèse, nous étudions des algorithmes pour un problème de recherche de relations à une ou plusieurs variables. Il généralise celui de calculer une solution à un système d’équations linéaires modulaires sur un anneau de polynômes, et inclut par exemple le calcul d’approximants de Hermite-Padé ou d’interpolants bivariés. Plutôt qu’une seule solution, nous nous attacherons à calculer un ensemble de générateurs possédant de bonnes propriétés. Précisément, l’entrée de notre problème consiste en un module de dimension finie spécifié par l’action des variables sur ses éléments, et en un certain nombre d’éléments de ce module ; il s’agit de calculer une base de Gröbner du modules des relations entre ces éléments. En termes d’algèbre linéaire, l’entrée décrit une matrice avec une structure de type Krylov, et il s’agit de calculer sous forme compacte une base du noyau de cette matrice. Nous proposons plusieurs algorithmes en fonction de la forme des matrices de multiplication qui représentent l’action des variables. Dans le cas d’une matrice de Jordan,nous accélérons le calcul d’interpolants multivariés sous certaines contraintes de degré ; nos résultats pour une forme de Frobenius permettent d’accélérer le calcul de formes normales de matrices polynomiales univariées. Enfin, dans le cas de plusieurs matrices denses, nous accélérons le changement d’ordre pour des bases de Gröbner d’idéaux multivariés zéro-dimensionnelsIn this thesis, we study algorithms for a problem of finding relations in one or several variables. It generalizes that of computing a solution to a system of linear modular equations over a polynomial ring, including in particular the computation of Hermite- Padéapproximants and bivariate interpolants. Rather than a single solution, we aim at computing generators of the solution set which have good properties. Precisely, the input of our problem consists of a finite-dimensional module given by the action of the variables on its elements, and of some elements of this module; the goal is to compute a Gröbner basis of the module of syzygies between these elements. In terms of linear algebra, the input describes a matrix with a type of Krylov structure, and the goal is to compute a compact representation of a basis of the nullspace of this matrix. We propose several algorithms in accordance with the structure of the multiplication matrices which specify the action of the variables. In the case of a Jordan matrix, we accelerate the computation of multivariate interpolants under degree constraints; our result for a Frobenius matrix leads to a faster algorithm for computing normal forms of univariate polynomial matrices. In the case of several dense matrices, we accelerate the change of monomial order for Gröbner bases of multivariate zero-dimensional ideals
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Tampango, Yendoubouam. "Développement d'une méthode sans maillage basée sur les approximations de Taylor." Thesis, Université de Lorraine, 2012. http://www.theses.fr/2012LORR0322/document.
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Ces dernières décennies, de nouvelles méthodes numériques connues sous le nom de « méthodes sans maillage » ont été développées. Contrairement à la MEF, ces méthodes n'utilisent qu'un ensemble de noeuds répartis dans le domaine sans demander un maillage de celui-ci. Jusqu'à présent, aucune de ces méthodes n'est parvenue à satisfaire les utilisateurs de la MEF. Dans cette thèse, nous proposons une méthode sans maillage, utilisant les approximations de Taylor. Cette méthode a l'avantage de n'utiliser que des points sur la frontière. En effet, l'EDP est résolue sous sa forme forte dans le domaine et les conditions aux limites sont appliquées par la méthode des moindres carrés. Cette méthode a été introduite, il y a 3 ans par S. Zeze dans sa thèse. Les tests académiques effectués en linéaire ont montré que cette méthode est très précise et que la convergence est améliorée en augmentant le degré, comme dans la p-version des EF. Nos travaux de thèse sont une suite des travaux de S. Zeze et ils visent à rendre plus robuste la méthode et aussi à élargir son champ d'application. Dans un premier temps, nous faisons une analyse mathématique de la méthode. Cette analyse passe par l'analyse des séries calculées. Le but de cette analyse est d'évaluer le domaine de convergence de la solution. Les résultats obtenus ont montré que pour certains problèmes, il faut subdiviser le domaine en quelques sous domaines et faire une résolution par sous domaine. La suite de nos travaux a donc été d'établir une technique de raccordement qui permettra d'assurer les conditions de transmission aux interfaces, dans le cas d'une résolution par sous domaine. En dernière partie, nous étendons l'application de la méthode aux problèmes non linéaires, en la couplant à une méthode de linéarisationIn these last decades, new numerical methods known as « meshless methods » have been developped. Contrary to the FEM, these methods uses only a set of nodes in the domain, without need of any mesh. Until now, any of these methods has convinced users of FEM. In this paper, we present a new meshless method using Taylor series expansion. In this method, the PDE is solved quasi exactly in the domain and the boundary conditions are applied by using a least square method. Then only the boundary discretisation is needed so the proposed method is a « true boundary meshless method ». This technique has been proposed for the first time by S. Zeze in his PhD thesis. The study of some linear problems has shown that this technique leads to a very good accuracy and that the convergence can be improved by increasing approximation degree. Our work is a continuation of S. Zeze work, and it consists to make the proposed method more robust and to extend its range of application. For that, we first make an analysis of the series computed by the method. The aim of this analysis was to evaluate the domain of validity of these series. This analysis showed that, for some problems, an accuracy cannot be obtained without splitting the domain in subdomains and making a resolution by subdomains. Therefore the second part of our work was to define a technique which will ensure the continuity at the interface between subdomains, in the case of a resolution by subdomains. The last part of our work was dedicated to non-linear problems. We establish an algorithm to show how the proposed method can deal with nonlinear-problems
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Wilkins, Janet Maureen. "Some aspects of simultaneous Pade approximation." Thesis, University of Kent, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.330243.
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Thiam, Ngueye. "Simulation des ondes lumineuses par une combinaison de la méthode de propagation par faisceaux et d'une discrétisation par éléments finis." Thesis, Université Laval, 2006. http://www.theses.ulaval.ca/2006/23711/23711.pdf.
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Miladi, Mohamed-Ali. "Récurrences linéaires et approximations simultanées de type Padé : applications à l'arithmétique." Lille 1, 2001. https://pepite-depot.univ-lille.fr/RESTREINT/Th_Num/2001/50376-2001-33.pdf.
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Nous établirons dans le chapitre 2 de cette thèse, un lien entre la méthode de Maeir et une identité binomiale et nous donnerons des approximations simultanées de type-Padé de certaines fonctions hypergéométriques. Dans le chapitre 3, nous déterminerons des mesures explicites d'indépendance linéaire de certains nombres représentant des valeurs de séries hypergéometriques prises en des points rationnels. Nous établirons dans le chapitre 4 et 5 des résultats d'indépendance linéaire sur Q de certains nombres représentant des valeurs de séries polylogarithmes prises en certains points rationnels. On aboutit aux résultats des chapitres 3, 4 et 5 en déterminant des approximations simultanées de type-Padé et en appliquant un théorème de Perron sur les récurrences linéaires. Dans le chapitre 6, on déterminera une nouvelle approximation simultanée de type-Padé de certaines séries hypergéométriques.
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Huttner, Marc. "Fonctions hypergéométriques et approximations diophantiennes." Lille 1, 1988. http://www.theses.fr/1988LIL10113.
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Cette thèse s'intéresse particulièrement aux approximations rationnelles des valeurs prises par des expressions faisant intervenir des fonctions hypergéométriques. Dans les divers articles qui la composent nous avons commencé par chercher des "approximant de pade" pour ces expressions. Pour cela, nous avons applique une idée de g. V. Chudnovsky qui consiste essentiellement à utiliser les propriétés des équations différentielles vérifiées par ces diverses fonctions analytiques. L'idée d'utiliser les propriétés des équations différentielles pour trouver des approximations rationnelles n'est pas nouvelle et remonte aux travaux de Riemann sur la fraction de gauss mais fune étude précise du reste et des polynômes intervenant dans le calcul de ces approximant utilisant le principe de monodromie nous a permis d'établir de nouvelles formules parfaitement exploitables du point de vue de l'arithmétique. Ceci nous a permis de trouver de nouvelles mesures d'irrationalité et d'indépendance linéaire pour des nombres algébriques qui améliorent de manière effective l'exposant de Liouville. On obtient aussi de nouvelles mesures d'irrationalité pour les constantes classiques de l'analyse.
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Roberts, Richard Peter. "Rational function approximations to unsteady aerodynamics." Thesis, University of Bristol, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.361136.
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Locht, Inka L. M. "Theoretical methods for the electronic structure and magnetism of strongly correlated materials." Doctoral thesis, Uppsala universitet, Materialteori, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-308699.
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In this work we study the interesting physics of the rare earths, and the microscopic state after ultrafast magnetization dynamics in iron. Moreover, this work covers the development, examination and application of several methods used in solid state physics. The first and the last part are related to strongly correlated electrons. The second part is related to the field of ultrafast magnetization dynamics. In the first part we apply density functional theory plus dynamical mean field theory within the Hubbard I approximation to describe the interesting physics of the rare-earth metals. These elements are characterized by the localized nature of the 4f electrons and the itinerant character of the other valence electrons. We calculate a wide range of properties of the rare-earth metals and find a good correspondence with experimental data. We argue that this theory can be the basis of future investigations addressing rare-earth based materials in general. In the second part of this thesis we develop a model, based on statistical arguments, to predict the microscopic state after ultrafast magnetization dynamics in iron. We predict that the microscopic state after ultrafast demagnetization is qualitatively different from the state after ultrafast increase of magnetization. This prediction is supported by previously published spectra obtained in magneto-optical experiments. Our model makes it possible to compare the measured data to results that are calculated from microscopic properties. We also investigate the relation between the magnetic asymmetry and the magnetization. In the last part of this work we examine several methods of analytic continuation that are used in many-body physics to obtain physical quantities on real energies from either imaginary time or Matsubara frequency data. In particular, we improve the Padé approximant method of analytic continuation. We compare the reliability and performance of this and other methods for both one and two-particle Green's functions. We also investigate the advantages of implementing a method of analytic continuation based on stochastic sampling on a graphics processing unit (GPU).
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Johnson, William Joel Dietmar. "Rational fraction approximations for passive network functions." [Tampa, Fla.] : University of South Florida, 2005. http://purl.fcla.edu/fcla/etd/SFE0001083.
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Essakhi, Brahim. "Modélisation électromagnétique 3D sur une large bande de fréquences par combinaison d'une méthode d'éléments finis et d'une approximation par fractions rationnelles : application aux structures rayonnantes." Paris 11, 2005. http://www.theses.fr/2005PA112151.
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Les outils de simulation numérique connaissent une utilisation intensive dans la résolution des problèmes de CEM. L'une des raisons est que la complexité croissante des problèmes à étudier rend l'expérimentation difficile à réaliser. De plus, les mesures ne peuvent être faites qu'en un nombre restreint de points de l'espace. La méthode des éléments finis a pour avantages de pouvoir aisément prendre en compte des géométries complexes et des milieux hétérogènes. Elle utilise un maillage conforme, qui s'adapte à la géométrie de la structure analysée et qui permet des raffinements locaux dans les régions où les variations des propriétés physiques, géométriques ou des champs sont plus importantes. Une formulation temporelle permet l'analyse de problèmes directement dans le domaine du temps. Une formulation fréquentielle conduit à résoudre un système linéaire pour chaque fréquence d'étude. Dans de nombreuses applications, les quantités électromagnétiques doivent être déterminées sur une large bande de fréquences et le système linéaire doit être résolu pour chaque fréquence d'intérêt. Ceci entraîne un coût de calcul important. Une alternative consiste à rechercher une approximation de la solution sous forme d'un développement en série ou d'une fraction rationnelle. Une approche possible consiste à développer la solution en série de Taylor autour d'une fréquence centrale. Le rayon de convergence de la série est limité mais il est possible d'étendre cet intervalle de validité en recourant à une approximation rationnelle de Padé. Une autre méthode consiste à rechercher une interpolation de la solution par fractions rationnelles, il s'agit de l'approximation de ChebyshevThe tools for digital simulation know an intensive use in the resolution of the problems of CEM. One of the reasons is that the increasing complexity of the problems to be studied makes the experimentation difficult to realize. Moreover, measurements cannot be made that in a restricted number of points of space. The finite element method has the advantages of easily being able to take into account complex geometries and heterogeneous mediums. It uses a grid in conformity, which adapts to the geometry of the analyzed structure and which allows local refinements in the areas where variations of the physical properties, geometrical or of the fields are more significant. A temporal formulation allows the analysis of problems directly in the field of time. A frequential formulation results in solving a linear system for each frequency of study. In many applications, the electromagnetic quantities must be given on a broad frequency band and the linear system must be solved for each frequency of interest. This involves a cost of significant calculation. An alternative consists in seeking an approximation of the solution in the form of a development in series or of a rational fraction. A possible approach consists in developing the solution in Taylor series around a centre frequency. The interval of convergence of the series is limited but it is possible to extend this interval of validity while resorting to a rational approximation of Padé. The approximation of Chebyshev is an other method based on rational approximation, it consists in seeking an interpolation of the solution
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Nguyen, Elitsa [Verfasser], Hans-Peter [Akademischer Betreuer] Blatt, and Ralitza [Akademischer Betreuer] Kovacheva. "Konvergenz reeller Tschebyscheff-, klassischer Padé- und Lp-Approximationen, p>1: Inverse Probleme / Elitsa Nguyen ; Hans-Peter Blatt, Ralitza Kovacheva." Eichstätt-Ingolstadt : Katholische Universität Eichstätt-Ingolstadt, 2018. http://d-nb.info/1156679192/34.
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Fischler, Stéphane. "Contributions à l'étude diophantienne des polylogarithmes et des groupes algébriques." Phd thesis, Université Pierre et Marie Curie - Paris VI, 2003. http://tel.archives-ouvertes.fr/tel-00002988.
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La première partie de la thèse porte sur l'irrationalité de valeurs de polylogarithmes. On exhibe des changements de variables entre intégrales multiples, qui généralisent les groupes de Rhin-Viola et relient les intégrales de Beukers et Vasilyev à celles de Sorokin. Puis, en commun avec Rivoal, on écrit comme solution unique d'un problème d'approximation de Padé une série hypergéométrique très générale. On en déduit notamment que l'un au moins des nombres $\Li_s(1/2)+\frac(\log(1/2)^s)((s-1)!)$, $s \in \(2,3,4\)$, est irrationnel. La seconde partie est consacrée à la transcendance dans les groupes algébriques. On démontre pour certaines variétés une conjecture de Roy (équivalente à la conjecture d'indépendance algébrique des logarithmes). Puis on prouve un lemme d'interpolation dans un groupe algébrique commutatif $G$, qui généralise celui de Masser en y incluant des multiplicités. Quand $G$ est linéaire, on exprime ce lemme et la dualité de Fourier-Borel en termes d'algèbres de Hopf.
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Ткаченко, И. Г., and В. В. Балабанова. "Аппроксимации Паде решений задач Коши." Thesis, Сумский государственный университет, 2014. http://essuir.sumdu.edu.ua/handle/123456789/39367.
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Al-Mohy, Awad. "Algorithms for the matrix exponential and its Fréchet derivative." Thesis, University of Manchester, 2011. https://www.research.manchester.ac.uk/portal/en/theses/algorithms-for-the-matrix-exponential-and-its-frechet-derivative(4de9bdbd-6d79-4e43-814a-197668694b8e).html.
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New algorithms for the matrix exponential and its Fréchet derivative are presented. First, we derive a new scaling and squaring algorithm (denoted expm[new]) for computing eA, where A is any square matrix, that mitigates the overscaling problem. The algorithm is built on the algorithm of Higham [SIAM J.Matrix Anal. Appl., 26(4): 1179-1193, 2005] but improves on it by two key features. The first, specific to triangular matrices, is to compute the diagonal elements in the squaring phase as exponentials instead of powering them. The second is to base the backward error analysis that underlies the algorithm on members of the sequence {||Ak||1/k} instead of ||A||. The terms ||Ak||1/k are estimated without computing powers of A by using a matrix 1-norm estimator. Second, a new algorithm is developed for computing the action of the matrix exponential on a matrix, etAB, where A is an n x n matrix and B is n x n₀ with n₀ << n. The algorithm works for any A, its computational cost is dominated by the formation of products of A with n x n₀ matrices, and the only input parameter is a backward error tolerance. The algorithm can return a single matrix etAB or a sequence etkAB on an equally spaced grid of points tk. It uses the scaling part of the scaling and squaring method together with a truncated Taylor series approximation to the exponential. It determines the amount of scaling and the Taylor degree using the strategy of expm[new].Preprocessing steps are used to reduce the cost of the algorithm. An important application of the algorithm is to exponential integrators for ordinary differential equations. It is shown that the sums of the form $\sum_{k=0}^p\varphi_k(A)u_k$ that arise in exponential integrators, where the $\varphi_k$ are related to the exponential function, can be expressed in terms of a single exponential of a matrix of dimension $n+p$ built by augmenting $A$ with additional rows and columns. Third, a general framework for simultaneously computing a matrix function, $f(A)$, and its Fréchet derivative in the direction $E$, $L_f(A,E)$, is established for a wide range of matrix functions. In particular, we extend the algorithm of Higham and $\mathrm{expm_{new}}$ to two algorithms that intertwine the evaluation of both $e^A$ and $L(A,E)$ at a cost about three times that for computing $e^A$ alone. These two extended algorithms are then adapted to algorithms that simultaneously calculate $e^A$ together with an estimate of its condition number. Finally, we show that $L_f(A,E)$, where $f$ is a real-valued matrix function and $A$ and $E$ are real matrices, can be approximated by $\Im f(A+ihE)/h$ for some suitably small $h$. This approximation generalizes the complex step approximation known in the scalar case, and is proved to be of second order in $h$ for analytic functions $f$ and also for the matrix sign function. It is shown that it does not suffer the inherent cancellation that limits the accuracy of finite difference approximations in floating point arithmetic. However, cancellation does nevertheless vitiate the approximation when the underlying method for evaluating $f$ employs complex arithmetic. The complex step approximation is attractive when specialized methods for evaluating the Fréchet derivative are not available.
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Adamík, Pavel. "Řízení dynamických systémů v reálném čase." Master's thesis, Vysoké učení technické v Brně. Fakulta informačních technologií, 2009. http://www.nusl.cz/ntk/nusl-236759.
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This thesis focuses on the methodology of controlling dynamic systems in real time. It contents a review of the control theory basis and the elementary base of regulators construction. Then the list of matemathic formulaes follows as well as the math basis for the system simulations using a difeerential count and the problem of difeerential equations solving. Furthermore, there is a systematic approach to the design of general regulator enclosed, using modern simulation techniques. After the results confirmation in the Matlab system, the problematics of transport delay & quantization modelling follow.
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弘毅, 田中, and Hiroki Tanaka. "電気鉄道き電システムの雷対策に向けた実測およびシミュレーション技術に関する一研究." Thesis, https://doors.doshisha.ac.jp/opac/opac_link/bibid/BB13044998/?lang=0, 2017. https://doors.doshisha.ac.jp/opac/opac_link/bibid/BB13044998/?lang=0.
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電気鉄道の安全安定輸送を確保するため，雷害防止が求められている。本論文では，電気鉄道設備の雷サージ特性実測を行い，接地インピーダンス特性を雷サージの視点から検討した。さらに，電力系統解析技術を応用して鉄道特有機器の回路解析モデルを開発し，その精度を実測で確認し，鉄道設備雷電流侵入時の応答を実測および計算結果より明らかにした。これらの成果は，電気鉄道の設計・保守・解析に十分に生かすことが可能である。Lightning protection is required to ensure safe and stable electric railway transportation. In this thesis, the lightning surge characteristics of the facilities in electric railway systems were measured. The characteristic of earthing impedance was also investigated from the viewpoint of lightning surge. In addition, some numerical models of railway specific apparatuses for circuit analysis method were developed by applying simulation technology for power system and confirmed their accuracies by actual measurements. The responses to lightning currents invaded into the facilities were clarified by the measured and calculated results. These results can be fully utilized in the design, maintenance and analysis of electric railway systems.
博士(工学)
Doctor of Philosophy in Engineering
同志社大学
Doshisha University
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Chou, Pʻing. "De Montessus de Ballore theorem for Pade approximation." Thesis, 1994. https://hdl.handle.net/10539/26388.
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A research report submitted to the Faculty of Science, University of the Witwatersrand,
Johannesburg, in partial fulfilment of the degree of Master of ScienceThe importance of Pade approximation has been increasingly recognized in ' recent years. The first convergence result of Pade approximants valid for general meromorphic functions was obtained by de Montessus de Ballore in 1902. He proved that when a function f has precisely n poles in I z 1< R, then the (n+ 1)th column in thePade table of f converges to f in I z J< R. (Abbreviation abstract)
Andrew Chakane 2019
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Graves-Morris, Peter R. "VPAStab: stabilised vector-Padé approximation with application to linear systems." 2003. http://hdl.handle.net/10454/3183.
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NoAn algorithm called VPAStab is given for the acceleration of convergence of a sequence of vectors. It combines a method of vector-Padé approximation with a successful technique for stabilisation. More generally, this algorithm is designed to find the fixed point of the generating function of the given sequence of vectors, analogously to the way in which ordinary Padé approximants can accelerate the convergence of a given scalar sequence. VPAStab is justified in the context of its application to the solution of a large sparse system of linear equations. The possible breakdowns of the algorithm are listed. Numerical experiments indicate that these breakdowns can be classified either as pivot-type (type L) or as ghost-type (type D).
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Tung, Lin Yuan, and 林沅東. "A log-MAP Algorithm with Padé Approximation for Turbo Code Decoding in CDMA Communications under Fading." Thesis, 2007. http://ndltd.ncl.edu.tw/handle/77723148493229093273.
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碩士大葉大學
電機工程學系
95
A novel log-MAP algorithm with Padé approximation to decode turbo code for CDMA communications under fading is presented in this paper. Numerical simulation are performed for the IS-2000 CDMA turbo code under Additive White Gaussian Noise (AWGN) and slow fading channels by using various log-MAP decoding algorithms. Results reveal that bit-error-rate (BER) performance of proposed Padé-approx-log-MAP algorithm is superior to those of previous log-MAP algorithms such as max-log-MAP, constant-log-MAP, and linear-log-MAP.
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Huang, Li-Shin, and 黃立昕. "Implementation of a Turbo-Code Decoder with Padé Approximation by Using the Dual-core MIPS-like Processor." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/56988026171103451718.
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碩士大葉大學
電機工程學系
98
Turbo coding offers excellent capabilities of error correction and thus has been getting popular in the wireless applications. Turbo codes demonstrate a means of closely approaching the Shannon capacity of communication channel. In this study, a Turbo-code decoder with Padé approximation using the dual-core RISC MIPS-like processor in association with the Verilog HDL and ASM is developed. A turbo-code codec with padé approximation is developed using Visual Basic language in this study. The encoded message from the codec designed by VB is imported the turbo-code decoder with padé approximation designed by C language for the verification. The C design of the turbo-code decoder is further compiled by GCC to generate the MIPS assembly. The machine code generated by PCSpim can be further embedded into shared memory of the dual-core MIPS-like processor designed by Verilog hardware description language and algorithmic state machine. The system simulation by using ModelSim and hardware verification by using FPGA are found to be correct. Finally, the MIPS-like processor is implemented with VLSI layout under TSMC 0.35μm process technology and to be able to produces the chipset in CIC. The main contribution of this study is using dual-core MIPS-like processor and integrating various EDA tools to achieve VLSI layout that the C design can be rapid prototyped in FPGA chip for verification. In this work, The bit-error-rate (BER) performance of proposed Padé-approx-log-MAP algorithm is superior to those of previous log-MAP algorithms such as max-log-MAP, constant-log-MAP, and linear-log-MAP.
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陳重嘉. "Implementation of a Turbo-Code Decoder with Padé Approximation by Using the Dual-core Processor and Hybrid Cloud." Thesis, 2017. http://ndltd.ncl.edu.tw/handle/3q25af.
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碩士大葉大學
電機工程學系
105
Cloud service offers easy access and low cost applications, and by combining Eucalyptus and Openshift cloud architectures we developed the platform. Turbo codes closely approach the Shannon capacity of communication channel and is used in this study. First we use Visual Basic language to develop a codec based on padé approximation to turbo-code and test if the algorithms function as desired. We then import the encoded message from the codec to the turbo-code decoder with padé approximation to turbo-code. The decoder is coded with C and first compiled by GCC to generate the assembly language, further generated the machine code by PCSpim, embedded into shared memory of the dual-core MIPS-like processor designed by Verilog hardware description language and algorithmic state machine. Software simulation by using ModelSim and hardware verification by using FPGA are verified. The MIPS-like processor is implemented with VLSI layout under TSMC 0.35μm process technology, and the chipset is produced in CIC.
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Graves-Morris, Peter R. "BiCGStab, VPAStab and an adaptation to mildly nonlinear systems." 2007. http://hdl.handle.net/10454/3622.
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NoThe key equations of BiCGStab are summarised to show its connections with Pade and vector-Pade approximation. These considerations lead naturally to stabilised vector-Pade approximation of a vector-valued function (VPAStab), and an algorithm for the acceleration of convergence of a linearly generated sequence of vectors. A generalisation of this algorithm for the acceleration of convergence of a nonlinearly generated system is proposed here, and comparative numerical results are given.
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Graves-Morris, Peter R., and A. Salam. "On the vector epsilon algorithm for solving linear systems of equations." 2009. http://hdl.handle.net/10454/2637.
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NoThe four vector extrapolation methods, minimal polynomial extrapolation, reduced rank extrapolation, modified minimal polynomial extrapolation and the topological epsilon algorithm, when applied to linearly generated vector sequences are Krylov subspace methods and it is known that they are equivalent to some well-known conjugate gradient type methods. However, the vector -algorithm is an extrapolation method, older than the four extrapolation methods above, and no similar results are known for it. In this paper, a determinantal formula for the vector -algorithm is given. Then it is shown that, when applied to a linearly generated vector sequence, the algorithm is also a Krylov subspace method and for a class of matrices the method is equivalent to a preconditioned Lanczos method. A new determinantal formula for the CGS is given, and an algebraic comparison between the vector -algorithm for linear systems and CGS is also given.
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(8964155), Ahmad Bassam Barhoumi. "ORTHOGONAL POLYNOMIALS ON S-CURVES ASSOCIATED WITH GENUS ONE SURFACES." Thesis, 2020.
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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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Ortgies, Gesa. "Ordnungssterne und Ordnungspfeile." 2011. https://ul.qucosa.de/id/qucosa%3A16457.
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Die Literatur von den Autoren Hairer, Wanner, Nørsett und Butcher, die der Arbeit als wichtige Quellen zugrunde lag, beschäftigt sich auch intensiv mit Mehrschrittverfahren.
Hier wird jeweils nur ein kurzer Ausblick auf Ordnungssterne bzw. Ordnungspfeile bei Mehrschrittverfahren mit einem Beispiel gegeben. Auch auf eine Behandlung der Ordnungssterne im Gebiet der Approximationstheorie wird mit einem Beispiel kurz hingewiesen.
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Liang, Jiaxi. "Approximating stable densities with Padé approximants and asymptotic series." Thesis, 2011. http://hdl.handle.net/10012/5886.
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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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Lin, Ching-Chang, and 林慶昌. "The S-wave Heavy Quarkonium Spectroscopy as Derived from the Pade Approximation." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/87155776436168216899.
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碩士中原大學
應用物理研究所
96
The S-wave c‾c charmonium spectroscopy has been calculated by considering thefull Hamiltonian in non-relativistic QCD (NRQCD), containing the next-to-leading order(NLO) corrections. The Hamiltonian for the binding energy of the charm and anti-charm pair is represented as ‾H (β) with β = 1. As shown in the paper, although the binding energy cannot be solved perturbatively, however, we find that its good approximation can be obtained by means of determining the Pad´e ratio from two extreme perturbative limits, β →∞ and β → 0. In numerical fit, four relevant physical parameters, the charm quark mass mc, strong coupling constant αs, charmed quark Compton wave lengthen 1/μ, and linear potential constant λ, can thus be determined. Our best fit results for the masses of the S-wave charmonium states are in good agreement with the current data. Some predictions can be further tested in the near future.
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SenWang, Jin, and 王勁森. "Modified Pade Analytical Approximation of Graphene Interband Conductivity for Finite-Difference Time-Domain Method." Thesis, 2017. http://ndltd.ncl.edu.tw/handle/98q3s6.
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Han-TingHuang and 黃漢廷. "Bound States in the Continuum for 2D Periodic nanostructures analyzed by Finite-difference Time-Domain method with Pade Approximation for high Q factor." Thesis, 2019. http://ndltd.ncl.edu.tw/handle/87r95p.
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碩士國立成功大學
光電科學與工程學系
107
Photonic bound states in the continuum (BIC) are found in photonic crystal structures with infinite lifetime or infinite cavity quality factor. This peculiar property is due to the coupling of certain guided resonant modes that leads the cancellation of radiation channels. BIC has great potential in the applications of lasers, sensors, and filters. The purpose of this study is to investigate and characteristics BIC in Plasmonic and dielectric structures by the Finite-difference time-domain (FDTD) method. First, single layered dielectric periodic structure is analyzed through the transmission spectrum to find the guided resonant mode. By shifting double layer dielectric periodic structure, a dark guided resonances mode which can be identified as BIC appears. Without shifting the double layered structure, an oblique angle incident excitation could also observe such BIC states. The Photonic Band structure is calculated to further analyze the appearance of the BIC states. Due to the infinite life time of BIC, it is difficult to analyze the quality factor of BIC. A combination of Padé approximant and Fast Fourier Transform (FFT) is developed to shorten the simulated time and obtain the correct cavity quality factors to help identifying BIC in FDTD calculation. Finally, a single layered metallic periodic structure is found to exhibit a quasi BIC state with propagating surface plasmon polaritons.