Newton's method is at the core of many algorithms used for solving nonlinear equations. A globalized Newton method is an implementation of Newton's method augmented with ``globalization procedures' intended to enhance the likelihood of convergence to a solution from an arbitrary initial guess. A Newton-GMRES method is an implementation of Newton's method in which the iterative linear algebra method GMRES is used to solve approximately the linear system that characterizes the Newton step. A globalized Newton-GMRES method combines both globalization procedures and the GMRES scheme to develop robust and efficient algorithms for solving nonlinear equations. The aim of this project is to describe the development of some globalized Newton-GMRES methods and to compare their performances on a few benchmark fluid flow problems.

[pt] A presente tese de doutorado trata do conceito de espaço em Leibniz, o qual sofreu algumas modificações ao longo da obra deste filósofo. A tese tenta mostrar, além disso, que, ao contrário do que afirmam alguns de seus comentadores no século XX, esse conceito diverge do conceito newtoniano de espaço, principalmente, no que diz respeito a seu aspecto metafísico, e não em seu aspecto físico, a propósito do qual ambos os filósofos estavam mais próximos do que se pensaria. A própria construção da física-matemática na era barroca aponta Descartes e os cartesianos, e não Newton, como o grande opositor de Leibniz. Em suma, procuramos mostrar que entre Leibniz e Newton, em torno do conceito de espaço, haveria divergências metafísicas e semelhanças físicas, ao mesmo tempo em que ambos divergiriam de Descartes. / [en] This doctoral dissertation deals with Leibniz s concept of space, which has undergone some changes over his writings. The dissertation also attempts to show that, contrary to the claims of some twentieth century commentators, this concept differs from the Newtonian concept of space mainly as regards to its metaphysical aspects, whereas as regards its physical aspects those philosophers were closer to each other than one might think. The very construction of mathematical physics in the Baroque era points to Descartes and the Cartesians, not Newton, as the great opponents of Leibniz. In short, we try to show that between Leibniz and Newton, as regards their concept of space, there are metaphysical differences as well as physical similarities, while both diverge from Descartes. / [fr] Cette thèse de doctorat traite du concept de l espace chez Leibniz, lequel a subi quelques changements au cours des travaux de ce philosophe. Nous essayons de montrer également que, contrairement aux allégations de certains commentateurs du XXe siècle, ce concept diffère de la conception newtonienne de l espace en ce qui concerne, essentiellement, son aspect métaphysique, mais non pas dans son aspect physique, sur lequel les deux philosophes étaient plus proches qu on pourrait penser. La construction même de la physique mathématique à l époque baroque indique Descartes et les cartésiens, non pas Newton, comme les grands adversaires de Leibniz. En bref, nous montrons que, en ce qui concerne le concept de l espace, il y aurait, entre Leibniz et Newton, des différences métaphysiques ainsi que des similitudes physiques, alors que les deux divergeraient de Descartes.

On étudie dans le corps des séries formelles de Puiseux, la résolution des équations algébriques de 2 et 3 variables. Le développement des solutions dépend de la nature du point au voisinage duquel on développe la fonction algébrique associée à cette équation algébrique. Pour les points réguliers on développe un algorithme basé sur la méthode itérative de Newton: xk+1=xk−f(xk)/f'(xk). Pour les points singuliers une méthode constructive appelée polygone de Newton permet de déterminer de proche en proche les approximants des solutions. On donne une application de la méthode du polygone de Newton à la détermination des polynômes facteurs déterminants d'un opérateur différentiel à singularité irrégulière à l'origine

Made available in DSpace on 2014-07-29T16:02:21Z (GMT). No. of bitstreams: 1 Dissertacao Max.pdf: 1036491 bytes, checksum: 23eaa8c8964b9edaac0cfd4d0c055564 (MD5) Previous issue date: 2007-12-14 / The search for solutions of nonlinear equations in the Euclidean spaces is object of interest in some areas of science and engineerings. Due the speed of convergence and computational efficiency, the inexact Newton method and its variations have been suficiently used to obtain solutions of these equations. In this dissertation we present a local analysis of convergence of the inexact Newton method and some of its variations, more specifically the inexact Newton-like method and the inexact modified Newton method. This analysis has the disadvantage to demand the previous knowledge of a zero of the operator in consideration and the hypotheses on the behavior of the operator at this zero, but on the other hand it supplies to information on the convergence rate and convergence radius. / A busca por soluçõeses de equaçõess não-lineares nos espaços Euclidianos é objeto de interesse em várias áreas da ciência e das engenharias. Devido a sua velocidade de convergência e e¯eficiência computacional, o método de Newton inexato e suas variações têm sido bastante utilizados para o propósito de obter solu»c~oes dessas equações. Nesta dissertação apresentamos uma anáalise de convergência local do método de Newton inexato e algumas de suas variações, mais especificamente, o método quase-Newton inexato e o método de Newton modificado inexato. Esta análise tem a desvantagem de exigir o conhecimento prévio de um zero do operador em consideração e hipóteses sobre o comportamento do operador nesse zero, mas por outro lado ela fornece informações sobre a taxa e o raio de convergência.

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This dissertation examines the preaching ministry of John Newton as a model of biblical exposition that was guided by a gospel-centric, pastoral homiletic. Chapter 1 defines the thesis of this dissertation , introduces the subject of this dissertation by surveying the scholarly work that has concentrated on Newton’s life and ministry, and demonstrates the lack of focused study on Newton’s preaching. Chapter 2 is a biographical survey of Newton’s life and ministry. Chapter 3 serves as an introduction to Newton’s preaching by surveying Newton’s sermons and demonstrates that Newton’s preaching should be regarded as expository. Attention is also given to the eighteenth-century historical context in which Newton preached. Chapter 4 argues that Newton’s high view of Scripture served as a foundation of his ministry and preaching. Chapter 5 is a discussion of Newton’s Christ-centered piety with regard to its impact on his life, ministry and preaching. Chapter 6 maintains that Newton’s Christ-centered spirituality is evident in his gospel-centric preaching and the homiletical methods that guided him. Chapter 7 examines Newton’s preaching and his commitment to pastoral ministry. It argues that Newton’s preaching rhetoric was a function of a pastoral homiletic that was deeply concerned with the spiritual welfare of his hearers. The final chapter summarizes the major points of dissertation and reflects on the importance of the use of historical models like Newton for contemporary preaching.

This work encompasses three parts. The first part provides a concise review of the most prominent metaheuristic concepts currently available and gives essential preliminaries together with definition of the combinatorial optimization problems. It substantiates the choice of the investigation direction and basis idea of the developed methods. In the second part the new nonlinear global optimization routines based on the TS strategy are described. The new approaches are the Gradient Tabu Search (GTS), the Gradient Only Tabu Search (GOTS), and the Tabu Search with Powell’s Algorithm (TSPA). In the last part of the work the GOTS is applied for such chemical optimization problems. The chapter provides a systematic approach how the variables are chosen and the adjustable parameters are set. As test cases the global minimum energy conformation of some amino acids, of two angiotensin converting enzyme (ACE) inhibitors, of 2-acetoxy-N,N,N-trimethylethanaminium, and of a HIV-1 protease inhibitor is determined. / Die Arbeit umfasst drei Kapitel. Das erste Kapitel stellt eine kurze Zusammenfassung über die bekanntesten, zurzeit verwendeten Metaheuristischen-Konzepte dar und gibt notwendige Einleitungen zusammen mit der Definition der kombinatorischen Optimierungsprobleme. Das Kapitel begründet die Wahl des Tabu-Ansatzes und diskutiert die Basisideen der entwickelten Methoden. Im zweiten Kapitel werden die neuen entwickelten, nichtlinearen Optimierungsroutinen beschrieben, die auf Tabu-Suchstrategien beruhen. Die neuen Algorithmen sind Gradient Tabu Search (GTS), Gradient Only Tabu Search (GOTS) und Tabu Search with Powell’s Algorithm (TSPA). Das letzte Kapitel der Arbeit beschreibt die Anwendung der GOTS Methode auf dieses Problem. Diskutiert werden die Auswahl der Variablen und die Einstellung der justierbaren Parameter. Die Effizienz der GOTS Methode wird an Hand einiger Aminosäuren, zwei Angiotensin-Derivaten (ACE-Hemmer), des Acetylcholin und eines HIV-1-Protease-Hemmstoff gezeigt.

Orientador: Ruben Aldrovandi / Mestre

This research examines an ordered perception rater model, an extension of the equal perception signal detection theory (SDT) latent class rater model. The expectation-maximization algorithm and the Newton-Raphson algorithm are used to estimate parameters. Four simulation studies are conducted to answer three research questions. Simulation studies 1 and 2 fit correct models to the data. Simulation study 1 generates one hundred data sets from the equal perception rater model, both with fully-crossed design and BIB design, and both without and with rater effects, and fits the equal perception model. Parameter recovery is excellent for fully-crossed design and reasonable for BIB design, and all rater effects are detected. Simulation study 2 generates one hundred simulated data sets from the ordered perception model, both with fully-crossed design and BIB design, and both without and with rater effects, and fits the ordered perception rater model. Although parameter recovery is biased for some parameters in the BIB design, all rater effects are recovered. Simulation studies 3 and 4 fit wrong models to the data. Simulation study 3 fits equal perception models to the fully-crossed and BIB ordered perception data sets generated in simulation study 2. All rater effects are revealed, although rater effects are distorted to some extent in the BIB design. Simulation study 4 fits ordered perception models to the fully-crossed and BIB equal perception data sets generated in study 1. All rater effects are recovered. Using essay scores from a large-scale language test, an empirical study is conducted. Both the equal and the ordered perception models are fitted. Information criteria favor the equal perception model.

There has been an increased interest in optimization for the analysis of large-scale data sets which require gigabytes or terabytes of data to be stored. A variety of applications originate from the fields of signal processing, machine learning and statistics. Seven representative applications are described below. - Magnetic Resonance Imaging (MRI): A medical imaging tool used to scan the anatomy and the physiology of a body. - Image inpainting: A technique for reconstructing degraded parts of an image. - Image deblurring: Image processing tool for removing the blurriness of a photo caused by natural phenomena, such as motion. - Radar pulse reconstruction. - Genome-Wide Association study (GWA): DNA comparison between two groups of people (with/without a disease) in order to investigate factors that a disease depends on. - Recommendation systems: Classification of data (i.e., music or video) based on user preferences. - Data fitting: Sampled data are used to simulate the behaviour of observed quantities. For example estimation of global temperature based on historic data. Large-scale problems impose restrictions on methods that have been so far employed. The new methods have to be memory efficient and ideally, within seconds they should offer noticeable progress towards a solution. First-order methods meet some of these requirements. They avoid matrix factorizations, they have low memory requirements, additionally, they sometimes offer fast progress in the initial stages of optimization. Unfortunately, as demonstrated by numerical experiments in this thesis, first-order methods miss essential information about the conditioning of the problems, which might result in slow practical convergence. The main advantage of first-order methods which is to rely only on simple gradient or coordinate updates becomes their essential weakness. We do not think this inherent weakness of first-order methods can be remedied. For this reason, the present thesis aims at the development and implementation of inexpensive higher-order methods for large-scale problems.