We present a new method for regularization of ill-conditioned problems that extends the traditional trust-region approach. Ill-conditioned problems arise, for example, in image restoration or mathematical processing of medical data, and involve matrices that are very ill-conditioned. The method makes use of the L-curve and L-curve maximum curvature criterion as a strategy recently proposed to find a good regularization parameter. We describe the method and show its application to an image restoration problem. We also provide a MATLAB code for the algorithm. Finally, a comparison to the CGLS approach is given and analyzed, and future research directions are proposed.

Thesis (M.S.)--Brigham Young University. Dept. of Mechanical Engineering, 2003. / Includes bibliographical references (p. 87-89).

Thesis (Ph.D.)--University of Tulsa, 1993. / Includes bibliographical references (leaves 254-269).

Thesis (M. Eng.)(Electronics)--University of Pretoria, 2001. / Title from opening screen (viewed March 10, 2005. Summaries in Afrikaans and English. Includes bibliography and index.

Thesis (Ph. D.)--Industrial and Systems Engineering, Georgia Institute of Technology, 2006. / Parker, R. Gary, Committee Member ; Shapiro, Alexander, Committee Member ; Nemirovski, Arkadi, Committee Member ; Green, William, Committee Member ; Monteiro, Renato, Committee Chair.

[pt] Desenvolve-se uma técnica para a extração de auto-pares relacionados com a solução de problemas de Elementos Finitos. O algoritmo consiste no uso dos métodos da Iteração Inversa e Gradiente Conjugado para a obtenção do vetor solução associado ao menor auto-valor. As soluções do auto-sistema são calculadas sequencialmente pela modificação da matriz dos coeficientes das equações de equilíbrio do problema através do uso de uma técnica de Deflação. O uso extensivo desta técnica introduz auto-valores múltiplos na matriz dos coeficientes, tornando necessário proceder-se a uma combinação dos dois métodos. É efetuado também um estudo para encontrar vetores iniciais apropriados a serem utilizados pelos métodos. O algoritmo foi implementado e alguns resultados de resolução de exemplos são apresentados, para ilustrar o seu desempenho. / [en] A vector iterative technique is developed for the extraction of eigenpairs related to the solution of finite element problems. The algorithm consists of using inverse iteration and conjugate gradient methods so as to obtain the solution vector associated to the smallest eigenvalue. Eigensolutions are sequentially calculated by replacing the coefficient matrix in the problem equilibrium equation using a deflation technique. The extensive usage of this technique, introduces multiple eigenvalue in the coefficient matrix, requiring a procedure to combine both methods. Also, a study is performed to find the appropriate starting vector to be used with methods. The algorithm has been implemented and the results of some example solutions are given that yield insight into its predictive capabilities.

Ce travail porte sur la détection de l’endommagement de matériaux composites. Une première partie concerne l’élaboration de méthodes permettant d’estimer les termes sources de chaleur d’un matériau sollicité mécaniquement. Lors de ce processus, un ensemble de défauts mécaniques mènent à des productions de chaleur. La détection des sources peut permettre la détection de ces défauts. Deux principales méthodes sont présentées : une méthode dite « directe » basée sur une discrétisation du champ de température mesuré et une méthode « itérative » basée sur la méthode du gradient conjugué. A ces méthodes sont couplées des techniques de filtrages des données comme la SVD. Les équations sont résolues par différences finies sous leur forme linéaire. Des modifications sont apportées à l’algorithme itératif pour améliorer sa convergence ainsi que les résultats. Les problématiques envisagées font partie des problèmes inverses en thermique. L’objectif de la première partie est de trouver un lien entre l’apparition de macro-fissure et la localisation de termes sources de chaleur au sein d’un matériau composite. La seconde partie consiste à élaborer des méthodes d’estimation des diffusivités thermiques directionnelles. Les méthodes reposent sur une modélisation du transfert de chaleur à l’aide des quadripôles thermiques. Les estimations de paramètres sont réalisées sur des zones ciblées à risque sur un matériau déjà endommagé. Le but est de faire le lien entre un endommagement mécanique connu diffus et une dégradation des propriétés thermiques. Ce manuscrit est présenté en deux parties : une partie de validation des méthodes. Une partie expérimentale où sont analysés les composites. / This work deals with the damage detection of composite materials. These materials are used in the aeronautics industry. The first part concerns the development of methods to estimate the heat sources terms of a stressed material. During this process, a set of mechanical defects leads to heat productions. The sources detection can conduct to the detection of these defects. Two main methods are presented: a "direct" method based on a discretization of the measured temperature field and an "iterative" method based on the conjugate gradient method. These methods are coupled with data filtering techniques such as SVD. In order to optimize computation time, equations are solved by finite differences in their linear form. Modifications are also made for the iterative algorithm to improve its convergence as well as the results of the estimation. These problems are considered as thermal inverse problems. The main objective of the first part is to find an experimental link between the appearance of a macro fissure and the localization of a heat source term within a composite material. The second part consists in the elaboration of methods for estimating thermal directional diffusivities. The methods are based on a modeling of heat transfer using thermal quadrupoles. Parameter estimations are made on targeted "risked" areas on a material, which is already damaged but not under stress. The aim is to link a known mechanical damage, which is called "diffuse" to thermal properties degradation in the main directions. This manuscript is presented in two parts: a validation part of the methods, and an experimental part in which composites are analyzed.

Submitted by Geandra Rodrigues (geandrar@gmail.com) on 2018-01-09T13:48:15Z No. of bitstreams: 1 renanpiazzarolifinottiamaral.pdf: 1172046 bytes, checksum: eb7bf10c813d64fbddcc572d39aecfc5 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2018-01-22T16:10:30Z (GMT) No. of bitstreams: 1 renanpiazzarolifinottiamaral.pdf: 1172046 bytes, checksum: eb7bf10c813d64fbddcc572d39aecfc5 (MD5) / Made available in DSpace on 2018-01-22T16:10:30Z (GMT). No. of bitstreams: 1 renanpiazzarolifinottiamaral.pdf: 1172046 bytes, checksum: eb7bf10c813d64fbddcc572d39aecfc5 (MD5) Previous issue date: 2017-09-01 / - / This thesis presents and discusses improvements in the type-1 and singleton fuzzy logic system for dealing with classification problems. Two training methods are addressed, the scaled conjugate gradient, which uses the second order information approximating the multiplication of the Hessian matrix H by the directional vector v (i.e. Hv), and the same method using the differential operator R {.} to compute the exact value of Hv. Also, in order to adapt the fuzzy model to handle multiclass classification problems, it is developed a novel fuzzy model with a vector as output. All proposals are tested through the performance metrics analysis based on data sets provided by UCI Machine Learning Repository. The reported results show the high convergence speed and better classification rates of the proposed training methods than others presented in the literature. Additionally, the novel fuzzy model has a significant reduction in computational and classifier complexity, especially when the number of classes in classification problem increases.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2016-03-31T14:47:16Z No. of bitstreams: 1 fellipelaraaparecida.pdf: 20651270 bytes, checksum: 48e88feb961f8d1446229cf83d322c3e (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-04-24T02:58:29Z (GMT) No. of bitstreams: 1 fellipelaraaparecida.pdf: 20651270 bytes, checksum: 48e88feb961f8d1446229cf83d322c3e (MD5) / Made available in DSpace on 2016-04-24T02:58:29Z (GMT). No. of bitstreams: 1 fellipelaraaparecida.pdf: 20651270 bytes, checksum: 48e88feb961f8d1446229cf83d322c3e (MD5) Previous issue date: 2013-04-30 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Este trabalho tem como objetivo o desenvolvimento de um código computacional para otimização de geometria de clusters metálicos. Para a otimização das coordenadas foi utilizado o método do gradiente conjugado não linear. Foi utilizado o potencial Tight- Binding com aproximação de segundos momentos (TB-SMA). As estruturas estudadas foram construídas nas direções cristalográficas fundamentais [1 0 0], [1 1 0] e [1 1 1]. Foi utilizado, também, o cálculo da função de distribuição radial para apresentar a goemetria das estruturas otimizadas. Um estudo complementar de compressão e alongamento foi realizado para as estruturas não otimizadas e otimizadas para verificar o comportamento das curvas de stress-strain das mesmas. Deste último estudo podese verificar uma situação limite em que estrutura sobrevive sem sofrer deformações permanentes. / This work aims to develop a computer code for geometry optimization of metal clusters. For the optimization of the coordinates we used the nonlinear conjugate gradient method. To describe the interactions between atoms we used the tight-binding potential with the second moments approximations (TB-SMA). The studied structures were built on the fundamental crystallographic directions [1 0 0] [1 1 0] and [1 1 1]. In order to elucidate good optimized structures we used the radial distribution function calculations. An additional study of compression and stretching was performed for the non-optimized and optimized structures to verify the behavior of the stressstrain curves. The stress-strain curves have shown the threshold situation in which the structures survives without permanet deformations.

A parallel realisation of the Conjugate Gradient Method with Schur-Complement preconditioning, based on a domain decomposition approach, is described in detail. Special kinds of solvers for the resulting interiour and coupling systems are presented. A large range of numerical results is used to demonstrate the properties and behaviour of this solvers in practical situations.