The main result of this thesis is the development of a theory of semidefinite facial reduction for the Euclidean distance matrix completion problem. Our key result shows a close connection between cliques in the graph of the partial Euclidean distance matrix and faces of the semidefinite cone containing the feasible set of the semidefinite relaxation. We show how using semidefinite facial reduction allows us to dramatically reduce the number of variables and constraints required to represent the semidefinite feasible set. We have used this theory to develop a highly efficient algorithm capable of solving many very large Euclidean distance matrix completion problems exactly, without the need for a semidefinite optimization solver. For problems with a low level of noise, our SNLSDPclique algorithm outperforms existing algorithms in terms of both CPU time and accuracy. Using only a laptop, problems of size up to 40,000 nodes can be solved in under a minute and problems with 100,000 nodes require only a few minutes to solve.

Recommendation systems are emerging as an important business application as the demand for personalized services in E-commerce increases. Collaborative filtering techniques are widely used for predicting a user's preference or generating a list of items to be recommended. In this thesis, we develop several new approaches for collaborative filtering based on model combination and kernel smoothing. Specifically, we start with an experimental study that compares a wide variety of CF methods under different conditions. Based on this study, we formulate a combination model similar to boosting but where the combination coefficients are functions rather than constant. In another contribution we formulate and analyze a local variation of matrix factorization. This formulation constructs multiple local matrix factorization models and then combines them into a global model. This formulation is based on the local low-rank assumption, a slightly different but more plausible assumption about the rating matrix. We apply this assumption to both rating prediction and ranking problems, with both empirical validations and theoretical analysis. We contribute with this thesis in four aspects. First, the local approaches we present significantly improve the accuracy of recommendations both in rating prediction and ranking problems. Second, with the more realistic local low-rank assumption, we fundamentally change the underlying assumption for matrix factorization-based recommendation systems. Third, we present highly efficient and scalable algorithms which take advantage of parallelism, suited for recent large scale datasets. Lastly, we provide an open source software implementing the local approaches in this thesis as well as many other recent recommendation algorithms, which can be used both in research and production.

The numerical solution of Stein (aka discrete Lyapunov) equations is the primary step in Newton's method for the solution of discrete-time algebraic Riccati equations (DARE). Here we present a low-rank Smith method as well as a low-rank alternating-direction-implicit-iteration to compute low-rank approximations to solutions of Stein equations arising in this context. Numerical results are given to verify the efficiency and accuracy of the proposed algorithms.

Um novo laboratório experimental desenvolvido para investigar a combustão de carvão em atmosferas de oxicombustão é descrito em detalhes na tese. Um reator ciclônico é utilizado para a combustão de carvões de baixo rank em condições de escoamento turbulento e com swirl, e operando em temperaturas similares às encontradas em câmaras de combustão industriais. Um sensor potenciométrico de oxigênio, instalado dentro do reator ciclônico, é utilizado para medir o consumo de oxigênio durante a combustão das amostras de carvão. Amostras de carvão com alto teor de cinzas, das minas do Leão e Bonito localizadas no sul do Brasil, e amostras de carvão linhito pré-seco (LTBK), da região da Lusácia, na Alemanha, foram submetidos à combustão em atmosferas de ar e de oxicombustão (O2/CO2/H2O). Os experimentos foram realizados em três temperaturas médias do gás de combustão: 1073, 1173 e 1273 K. Para as amostras do carvão LTBK, a oxicombustão foi composta com duas atmosferas de O2/CO2 sem vapor d’água (21/79 e 30/70) e três atmosferas de O2/CO2/H2O (30/60/10, 30/50/20 e 30/40/30) em base molar, enquanto para as amostras dos carvões Leão e Bonito, a oxicombustão foi composta com duas atmosferas de O2/CO2 (21/79 e 30/70). As amostras de carvão foram peneiradas para uma faixa de tamanho de partículas de 1250 a 2000 μm e 125 a 500 μm, e com massas de 1g e 3g. Em adição aos testes, amostras de char dos carvões Leão e LTBK foram preparadas para investigar o comportamento da combustão de suas matrizes carbonosas com diferentes níveis de matéria volátil. Primeiramente, a investigação da combustão do carvão é feita diretamente a partir das curvas de concentração de oxigênio medidas para a combustão das amostras de carvão LTBK submetidos às atmosferas de ar e oxicombustão com vapor d’água, conforme explicado no Capítulo 2 desta tese. Entretanto, devido ao grande número de experimentos realizados e a necessidade de entender a influência dos fatores, como temperatura e as composições das atmosferas oxidantes, e as interações entre esses fatores na combustão do carvão, a análise pela metodologia do Projeto de Experimentos (DoE) é aplicada nos experimentos, conforme detalhado no Capítulo 3. A reatividade dos carvões de baixo rank é investigada por meio do cálculo dos parâmetros cinéticos globais e dos coeficientes da taxa de reação de combustão do char, considerando a hipótese de um reator bem misturado, a ser verificada ao longo da investigação, conforme descrito no Capítulo 4. A partir da análise das curvas de concentração de oxigênio (Capítulos 2 e 3), os resultados mostram que a atmosfera de oxicombustão com 79% de CO2 (21/79, O2/CO2) aumenta o consumo de oxigênio para os carvões de alto teor de cinzas, Bonito e Leão, e para o carvão linhito com alto teor de voláteis (LTBK), devido à influência da reação de gaseificação do CO2 a partir de temperaturas acima de 1073 K. A partir da análise dos parâmetros cinéticos globais calculados para avaliar a reatividade dos carvões, os resultados mostram que a hipótese do reator bem misturado não é o suficiente para capturar a cinética da combustão do carvão por batelada no interior do reator ciclônico. A reatividade dos carvões investigados, através das constantes efetivas da taxa de reação, variando-se a composição da atmosfera oxidante, temperatura do gás de combustão, tamanho de partículas, massa da amostra e posição do sensor de oxigênio, têm influência do escoamento com swirl e seus termos advectivos e difusivos. / A novel laboratory facility designed to investigate coal oxy-fuel combustion is described in the present work. A cyclone chamber allows for the combustion of low-rank coal under turbulent conditions and swirling flows, covering a temperature range similar to those found on practical furnaces. A potentiometric oxygen sensor with oxide-ion conducting solid electrolytes, as stabilized zirconia, installed within the cyclone reactor, is used to measure the oxygen consumption during the combustion of coal samples. High ash coals samples, from Leão and Bonito mining sites located in South Brazil, and pre-dried lignite coal samples (LTBK), from the Lusatian region, in Germany, were burned under air and oxy-fuel (O2/CO2/H2O) atmospheres. Experiments were carried out at three average gas combustion temperatures: 1073, 1173 and 1273 K. For LTBK coal, oxy-fuel combustion was composed with two O2/CO2 atmospheres (21/79 and 30/70) and three O2/CO2/H2O atmospheres (30/60/10, 30/50/20 and 30/40/30) in molar basis, whereas for Leão and Bonito coals, the oxy-fuel combustion was composed with two O2/CO2 atmospheres (21/79 and 30/70). Coal samples were sieved to a size range of 1250 to 2000 μm and 125 to 500 μm and with 1g and 3g. In addition, char samples from Leão and lignite coals were prepared in order to investigate the combustion behavior of its carbon matrix for different levels of volatile matter. The investigation of coal combustion behavior is made firstly directly on the oxygen concentration curves measured for LTBK coal samples burned under air and oxy-fuel atmospheres with water vapor, as detailed in Chapter 2 of this thesis. However, due to the great number of experiments performed and the need to understand the influence of the factors, as temperature and atmosphere compositions, and the interactions between them on the coal combustion, the Design of Experiments (DoE) analysis is applied in the laboratory test facility, as developed in Chapter 3. The reactivity of low rank coals is assessed by means of global kinetic parameters and of char combustion reaction coefficients, under assumption of a well stirred reactor to be tested along the investigation, as described in Chapter 4. From the analysis of oxygen concentration curves (Chapter 2 and 3), results show that oxidizer oxy-fuel atmosphere with 79% CO2 (21/79, O2/CO2) increases the oxygen consumption for high ash coals, Bonito and Leão, and for pre-dried lignite coal, LTBK, due to the influence of CO2 gasification reaction on their coal combustion reactions from gas combustion temperatures higher than 1073 K. From the analysis of global kinetic parameters calculated to assess the coal reactivity, the results show that the hypothesis of a well stirred reactor is not enough to capture the kinetic involved in coal combustion burned in batch mode within the cyclone reactor. The coal reactivity investigated with the effective reaction rate constants for different oxidizer atmospheres, gas combustion temperatures, particle diameters, sample masses and oxygen sensor position, is influenced by the swirling flow with its advective and diffusive terms.

Um novo laboratório experimental desenvolvido para investigar a combustão de carvão em atmosferas de oxicombustão é descrito em detalhes na tese. Um reator ciclônico é utilizado para a combustão de carvões de baixo rank em condições de escoamento turbulento e com swirl, e operando em temperaturas similares às encontradas em câmaras de combustão industriais. Um sensor potenciométrico de oxigênio, instalado dentro do reator ciclônico, é utilizado para medir o consumo de oxigênio durante a combustão das amostras de carvão. Amostras de carvão com alto teor de cinzas, das minas do Leão e Bonito localizadas no sul do Brasil, e amostras de carvão linhito pré-seco (LTBK), da região da Lusácia, na Alemanha, foram submetidos à combustão em atmosferas de ar e de oxicombustão (O2/CO2/H2O). Os experimentos foram realizados em três temperaturas médias do gás de combustão: 1073, 1173 e 1273 K. Para as amostras do carvão LTBK, a oxicombustão foi composta com duas atmosferas de O2/CO2 sem vapor d’água (21/79 e 30/70) e três atmosferas de O2/CO2/H2O (30/60/10, 30/50/20 e 30/40/30) em base molar, enquanto para as amostras dos carvões Leão e Bonito, a oxicombustão foi composta com duas atmosferas de O2/CO2 (21/79 e 30/70). As amostras de carvão foram peneiradas para uma faixa de tamanho de partículas de 1250 a 2000 μm e 125 a 500 μm, e com massas de 1g e 3g. Em adição aos testes, amostras de char dos carvões Leão e LTBK foram preparadas para investigar o comportamento da combustão de suas matrizes carbonosas com diferentes níveis de matéria volátil. Primeiramente, a investigação da combustão do carvão é feita diretamente a partir das curvas de concentração de oxigênio medidas para a combustão das amostras de carvão LTBK submetidos às atmosferas de ar e oxicombustão com vapor d’água, conforme explicado no Capítulo 2 desta tese. Entretanto, devido ao grande número de experimentos realizados e a necessidade de entender a influência dos fatores, como temperatura e as composições das atmosferas oxidantes, e as interações entre esses fatores na combustão do carvão, a análise pela metodologia do Projeto de Experimentos (DoE) é aplicada nos experimentos, conforme detalhado no Capítulo 3. A reatividade dos carvões de baixo rank é investigada por meio do cálculo dos parâmetros cinéticos globais e dos coeficientes da taxa de reação de combustão do char, considerando a hipótese de um reator bem misturado, a ser verificada ao longo da investigação, conforme descrito no Capítulo 4. A partir da análise das curvas de concentração de oxigênio (Capítulos 2 e 3), os resultados mostram que a atmosfera de oxicombustão com 79% de CO2 (21/79, O2/CO2) aumenta o consumo de oxigênio para os carvões de alto teor de cinzas, Bonito e Leão, e para o carvão linhito com alto teor de voláteis (LTBK), devido à influência da reação de gaseificação do CO2 a partir de temperaturas acima de 1073 K. A partir da análise dos parâmetros cinéticos globais calculados para avaliar a reatividade dos carvões, os resultados mostram que a hipótese do reator bem misturado não é o suficiente para capturar a cinética da combustão do carvão por batelada no interior do reator ciclônico. A reatividade dos carvões investigados, através das constantes efetivas da taxa de reação, variando-se a composição da atmosfera oxidante, temperatura do gás de combustão, tamanho de partículas, massa da amostra e posição do sensor de oxigênio, têm influência do escoamento com swirl e seus termos advectivos e difusivos. / A novel laboratory facility designed to investigate coal oxy-fuel combustion is described in the present work. A cyclone chamber allows for the combustion of low-rank coal under turbulent conditions and swirling flows, covering a temperature range similar to those found on practical furnaces. A potentiometric oxygen sensor with oxide-ion conducting solid electrolytes, as stabilized zirconia, installed within the cyclone reactor, is used to measure the oxygen consumption during the combustion of coal samples. High ash coals samples, from Leão and Bonito mining sites located in South Brazil, and pre-dried lignite coal samples (LTBK), from the Lusatian region, in Germany, were burned under air and oxy-fuel (O2/CO2/H2O) atmospheres. Experiments were carried out at three average gas combustion temperatures: 1073, 1173 and 1273 K. For LTBK coal, oxy-fuel combustion was composed with two O2/CO2 atmospheres (21/79 and 30/70) and three O2/CO2/H2O atmospheres (30/60/10, 30/50/20 and 30/40/30) in molar basis, whereas for Leão and Bonito coals, the oxy-fuel combustion was composed with two O2/CO2 atmospheres (21/79 and 30/70). Coal samples were sieved to a size range of 1250 to 2000 μm and 125 to 500 μm and with 1g and 3g. In addition, char samples from Leão and lignite coals were prepared in order to investigate the combustion behavior of its carbon matrix for different levels of volatile matter. The investigation of coal combustion behavior is made firstly directly on the oxygen concentration curves measured for LTBK coal samples burned under air and oxy-fuel atmospheres with water vapor, as detailed in Chapter 2 of this thesis. However, due to the great number of experiments performed and the need to understand the influence of the factors, as temperature and atmosphere compositions, and the interactions between them on the coal combustion, the Design of Experiments (DoE) analysis is applied in the laboratory test facility, as developed in Chapter 3. The reactivity of low rank coals is assessed by means of global kinetic parameters and of char combustion reaction coefficients, under assumption of a well stirred reactor to be tested along the investigation, as described in Chapter 4. From the analysis of oxygen concentration curves (Chapter 2 and 3), results show that oxidizer oxy-fuel atmosphere with 79% CO2 (21/79, O2/CO2) increases the oxygen consumption for high ash coals, Bonito and Leão, and for pre-dried lignite coal, LTBK, due to the influence of CO2 gasification reaction on their coal combustion reactions from gas combustion temperatures higher than 1073 K. From the analysis of global kinetic parameters calculated to assess the coal reactivity, the results show that the hypothesis of a well stirred reactor is not enough to capture the kinetic involved in coal combustion burned in batch mode within the cyclone reactor. The coal reactivity investigated with the effective reaction rate constants for different oxidizer atmospheres, gas combustion temperatures, particle diameters, sample masses and oxygen sensor position, is influenced by the swirling flow with its advective and diffusive terms.

Um novo laboratório experimental desenvolvido para investigar a combustão de carvão em atmosferas de oxicombustão é descrito em detalhes na tese. Um reator ciclônico é utilizado para a combustão de carvões de baixo rank em condições de escoamento turbulento e com swirl, e operando em temperaturas similares às encontradas em câmaras de combustão industriais. Um sensor potenciométrico de oxigênio, instalado dentro do reator ciclônico, é utilizado para medir o consumo de oxigênio durante a combustão das amostras de carvão. Amostras de carvão com alto teor de cinzas, das minas do Leão e Bonito localizadas no sul do Brasil, e amostras de carvão linhito pré-seco (LTBK), da região da Lusácia, na Alemanha, foram submetidos à combustão em atmosferas de ar e de oxicombustão (O2/CO2/H2O). Os experimentos foram realizados em três temperaturas médias do gás de combustão: 1073, 1173 e 1273 K. Para as amostras do carvão LTBK, a oxicombustão foi composta com duas atmosferas de O2/CO2 sem vapor d’água (21/79 e 30/70) e três atmosferas de O2/CO2/H2O (30/60/10, 30/50/20 e 30/40/30) em base molar, enquanto para as amostras dos carvões Leão e Bonito, a oxicombustão foi composta com duas atmosferas de O2/CO2 (21/79 e 30/70). As amostras de carvão foram peneiradas para uma faixa de tamanho de partículas de 1250 a 2000 μm e 125 a 500 μm, e com massas de 1g e 3g. Em adição aos testes, amostras de char dos carvões Leão e LTBK foram preparadas para investigar o comportamento da combustão de suas matrizes carbonosas com diferentes níveis de matéria volátil. Primeiramente, a investigação da combustão do carvão é feita diretamente a partir das curvas de concentração de oxigênio medidas para a combustão das amostras de carvão LTBK submetidos às atmosferas de ar e oxicombustão com vapor d’água, conforme explicado no Capítulo 2 desta tese. Entretanto, devido ao grande número de experimentos realizados e a necessidade de entender a influência dos fatores, como temperatura e as composições das atmosferas oxidantes, e as interações entre esses fatores na combustão do carvão, a análise pela metodologia do Projeto de Experimentos (DoE) é aplicada nos experimentos, conforme detalhado no Capítulo 3. A reatividade dos carvões de baixo rank é investigada por meio do cálculo dos parâmetros cinéticos globais e dos coeficientes da taxa de reação de combustão do char, considerando a hipótese de um reator bem misturado, a ser verificada ao longo da investigação, conforme descrito no Capítulo 4. A partir da análise das curvas de concentração de oxigênio (Capítulos 2 e 3), os resultados mostram que a atmosfera de oxicombustão com 79% de CO2 (21/79, O2/CO2) aumenta o consumo de oxigênio para os carvões de alto teor de cinzas, Bonito e Leão, e para o carvão linhito com alto teor de voláteis (LTBK), devido à influência da reação de gaseificação do CO2 a partir de temperaturas acima de 1073 K. A partir da análise dos parâmetros cinéticos globais calculados para avaliar a reatividade dos carvões, os resultados mostram que a hipótese do reator bem misturado não é o suficiente para capturar a cinética da combustão do carvão por batelada no interior do reator ciclônico. A reatividade dos carvões investigados, através das constantes efetivas da taxa de reação, variando-se a composição da atmosfera oxidante, temperatura do gás de combustão, tamanho de partículas, massa da amostra e posição do sensor de oxigênio, têm influência do escoamento com swirl e seus termos advectivos e difusivos. / A novel laboratory facility designed to investigate coal oxy-fuel combustion is described in the present work. A cyclone chamber allows for the combustion of low-rank coal under turbulent conditions and swirling flows, covering a temperature range similar to those found on practical furnaces. A potentiometric oxygen sensor with oxide-ion conducting solid electrolytes, as stabilized zirconia, installed within the cyclone reactor, is used to measure the oxygen consumption during the combustion of coal samples. High ash coals samples, from Leão and Bonito mining sites located in South Brazil, and pre-dried lignite coal samples (LTBK), from the Lusatian region, in Germany, were burned under air and oxy-fuel (O2/CO2/H2O) atmospheres. Experiments were carried out at three average gas combustion temperatures: 1073, 1173 and 1273 K. For LTBK coal, oxy-fuel combustion was composed with two O2/CO2 atmospheres (21/79 and 30/70) and three O2/CO2/H2O atmospheres (30/60/10, 30/50/20 and 30/40/30) in molar basis, whereas for Leão and Bonito coals, the oxy-fuel combustion was composed with two O2/CO2 atmospheres (21/79 and 30/70). Coal samples were sieved to a size range of 1250 to 2000 μm and 125 to 500 μm and with 1g and 3g. In addition, char samples from Leão and lignite coals were prepared in order to investigate the combustion behavior of its carbon matrix for different levels of volatile matter. The investigation of coal combustion behavior is made firstly directly on the oxygen concentration curves measured for LTBK coal samples burned under air and oxy-fuel atmospheres with water vapor, as detailed in Chapter 2 of this thesis. However, due to the great number of experiments performed and the need to understand the influence of the factors, as temperature and atmosphere compositions, and the interactions between them on the coal combustion, the Design of Experiments (DoE) analysis is applied in the laboratory test facility, as developed in Chapter 3. The reactivity of low rank coals is assessed by means of global kinetic parameters and of char combustion reaction coefficients, under assumption of a well stirred reactor to be tested along the investigation, as described in Chapter 4. From the analysis of oxygen concentration curves (Chapter 2 and 3), results show that oxidizer oxy-fuel atmosphere with 79% CO2 (21/79, O2/CO2) increases the oxygen consumption for high ash coals, Bonito and Leão, and for pre-dried lignite coal, LTBK, due to the influence of CO2 gasification reaction on their coal combustion reactions from gas combustion temperatures higher than 1073 K. From the analysis of global kinetic parameters calculated to assess the coal reactivity, the results show that the hypothesis of a well stirred reactor is not enough to capture the kinetic involved in coal combustion burned in batch mode within the cyclone reactor. The coal reactivity investigated with the effective reaction rate constants for different oxidizer atmospheres, gas combustion temperatures, particle diameters, sample masses and oxygen sensor position, is influenced by the swirling flow with its advective and diffusive terms.

No description available.

Ground penetrating radar (GPR) has been extensively utilized as a highly efficient and non-destructive testing method for infrastructure evaluation, such as highway rebar detection, bridge decks inspection, asphalt pavement monitoring, underground pipe leakage detection, railroad ballast assessment, etc. The focus of this dissertation is to investigate the key techniques to tackle with GPR signal processing from three perspectives: (1) Removing or suppressing the radar clutter signal; (2) Detecting the underground target or the region of interest (RoI) in the GPR image; (3) Imaging the underground target to eliminate or alleviate the feature distortion and reconstructing the shape of the target with good fidelity. In the first part of this dissertation, a low-rank and sparse representation based approach is designed to remove the clutter produced by rough ground surface reflection for impulse radar. In the second part, Hilbert Transform and 2-D Renyi entropy based statistical analysis is explored to improve RoI detection efficiency and to reduce the computational cost for more sophisticated data post-processing. In the third part, a back-projection imaging algorithm is designed for both ground-coupled and air-coupled multistatic GPR configurations. Since the refraction phenomenon at the air-ground interface is considered and the spatial offsets between the transceiver antennas are compensated in this algorithm, the data points collected by receiver antennas in time domain can be accurately mapped back to the spatial domain and the targets can be imaged in the scene space under testing. Experimental results validate that the proposed three-stage cascade signal processing methodologies can improve the performance of GPR system.

This thesis focuses on two topics, computational methods for large spatial datasets and functional data ranking. Both are tackling the challenges of big and high-dimensional data. The first topic is motivated by the prohibitive computational burden in fitting Gaussian process models to large and irregularly spaced spatial datasets. Various approximation methods have been introduced to reduce the computational cost, but many rely on unrealistic assumptions about the process and retaining statistical efficiency remains an issue. We propose a new scheme to approximate the maximum likelihood estimator and the kriging predictor when the exact computation is infeasible. The proposed method provides different types of hierarchical low-rank approximations that are both computationally and statistically efficient. We explore the improvement of the approximation theoretically and investigate the performance by simulations. For real applications, we analyze a soil moisture dataset with 2 million measurements with the hierarchical low-rank approximation and apply the proposed fast kriging to fill gaps for satellite images. The second topic is motivated by rank-based outlier detection methods for functional data. Compared to magnitude outliers, it is more challenging to detect shape outliers as they are often masked among samples. We develop a new notion of functional data depth by taking the integration of a univariate depth function. Having a form of the integrated depth, it shares many desirable features. Furthermore, the novel formation leads to a useful decomposition for detecting both shape and magnitude outliers. Our simulation studies show the proposed outlier detection procedure outperforms competitors in various outlier models. We also illustrate our methodology using real datasets of curves, images, and video frames. Finally, we introduce the functional data ranking technique to spatio-temporal statistics for visualizing and assessing covariance properties, such as separability and full symmetry. We formulate test functions as functions of temporal lags for each pair of spatial locations and develop a rank-based testing procedure induced by functional data depth for assessing these properties. The method is illustrated using simulated data from widely used spatio-temporal covariance models, as well as real datasets from weather stations and climate model outputs.

El tema principal de esta tesis es el desarrollo de técnicas de actualización de precondicionadores para resolver sistemas lineales de gran tamaño y dispersos Ax=b mediante el uso de métodos iterativos de Krylov. Se consideran dos tipos interesantes de problemas. En el primero se estudia la solución iterativa de sistemas lineales no singulares y antisimétricos, donde la matriz de coeficientes A tiene parte antisimétrica de rango bajo o puede aproximarse bien con una matriz antisimétrica de rango bajo. Sistemas como este surgen de la discretización de PDEs con ciertas condiciones de frontera de Neumann, la discretización de ecuaciones integrales y métodos de puntos interiores, por ejemplo, el problema de Bratu y la ecuación integral de Love. El segundo tipo de sistemas lineales considerados son problemas de mínimos cuadrados (LS) que se resuelven considerando la solución del sistema equivalente de ecuaciones normales. Concretamente, consideramos la solución de problemas LS modificados y de rango incompleto. Por problema LS modificado se entiende que el conjunto de ecuaciones lineales se actualiza con alguna información nueva, se agrega una nueva variable o, por el contrario, se elimina alguna información o variable del conjunto. En los problemas LS de rango deficiente, la matriz de coeficientes no tiene rango completo, lo que dificulta el cálculo de una factorización incompleta de las ecuaciones normales. Los problemas LS surgen en muchas aplicaciones a gran escala de la ciencia y la ingeniería como, por ejemplo, redes neuronales, programación lineal, sismología de exploración o procesamiento de imágenes. Los precondicionadores directos para métodos iterativos usados habitualmente son las factorizaciones incompletas LU, o de Cholesky cuando la matriz es simétrica definida positiva. La principal contribución de esta tesis es el desarrollo de técnicas de actualización de precondicionadores. Básicamente, el método consiste en el cálculo de una descomposición incompleta para un sistema lineal aumentado equivalente, que se utiliza como precondicionador para el problema original. El estudio teórico y los resultados numéricos presentados en esta tesis muestran el rendimiento de la técnica de precondicionamiento propuesta y su competitividad en comparación con otros métodos disponibles en la literatura para calcular precondicionadores para los problemas estudiados. / The main topic of this thesis is updating preconditioners for solving large sparse linear systems Ax=b by using Krylov iterative methods. Two interesting types of problems are considered. In the first one is studied the iterative solution of non-singular, non-symmetric linear systems where the coefficient matrix A has a skew-symmetric part of low-rank or can be well approximated with a skew-symmetric low-rank matrix. Systems like this arise from the discretization of PDEs with certain Neumann boundary conditions, the discretization of integral equations as well as path following methods, for example, the Bratu problem and the Love's integral equation. The second type of linear systems considered are least squares (LS) problems that are solved by considering the solution of the equivalent normal equations system. More precisely, we consider the solution of modified and rank deficient LS problems. By modified LS problem, it is understood that the set of linear relations is updated with some new information, a new variable is added or, contrarily, some information or variable is removed from the set. Rank deficient LS problems are characterized by a coefficient matrix that has not full rank, which makes difficult the computation of an incomplete factorization of the normal equations. LS problems arise in many large-scale applications of the science and engineering as for instance neural networks, linear programming, exploration seismology or image processing. Usually, incomplete LU or incomplete Cholesky factorization are used as preconditioners for iterative methods. The main contribution of this thesis is the development of a technique for updating preconditioners by bordering. It consists in the computation of an approximate decomposition for an equivalent augmented linear system, that is used as preconditioner for the original problem. The theoretical study and the results of the numerical experiments presented in this thesis show the performance of the preconditioner technique proposed and its competitiveness compared with other methods available in the literature for computing preconditioners for the problems studied. / El tema principal d'esta tesi és actualitzar precondicionadors per a resoldre sistemes lineals grans i buits Ax=b per mitjà de l'ús de mètodes iteratius de Krylov. Es consideren dos tipus interessants de problemes. En el primer s'estudia la solució iterativa de sistemes lineals no singulars i antisimètrics, on la matriu de coeficients A té una part antisimètrica de baix rang, o bé pot aproximar-se amb una matriu antisimètrica de baix rang. Sistemes com este sorgixen de la discretització de PDEs amb certes condicions de frontera de Neumann, la discretització d'equacions integrals i mètodes de punts interiors, per exemple, el problema de Bratu i l'equació integral de Love. El segon tipus de sistemes lineals considerats, són problemes de mínims quadrats (LS) que es resolen considerant la solució del sistema equivalent d'equacions normals. Concretament, considerem la solució de problemes de LS modificats i de rang incomplet. Per problema LS modificat, s'entén que el conjunt d'equacions lineals s'actualitza amb alguna informació nova, s'agrega una nova variable o, al contrari, s'elimina alguna informació o variable del conjunt. En els problemes LS de rang deficient, la matriu de coeficients no té rang complet, la qual cosa dificultata el calcul d'una factorització incompleta de les equacions normals. Els problemes LS sorgixen en moltes aplicacions a gran escala de la ciència i l'enginyeria com, per exemple, xarxes neuronals, programació lineal, sismologia d'exploració o processament d'imatges. Els precondicionadors directes per a mètodes iteratius utilitzats més a sovint són les factoritzacions incompletes tipus ILU, o la factorització incompleta de Cholesky quan la matriu és simètrica definida positiva. La principal contribució d'esta tesi és el desenvolupament de tècniques d'actualització de precondicionadors. Bàsicament, el mètode consistix en el càlcul d'una descomposició incompleta per a un sistema lineal augmentat equivalent, que s'utilitza com a precondicionador pel problema original. L'estudi teòric i els resultats numèrics presentats en esta tesi mostren el rendiment de la tècnica de precondicionament proposta i la seua competitivitat en comparació amb altres mètodes disponibles en la literatura per a calcular precondicionadors per als problemes considerats. / Guerrero Flores, DJ. (2018). On Updating Preconditioners for the Iterative Solution of Linear Systems [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/104923 / TESIS