La résolution de systèmes linéaires creux est un problème qui apparaît dans de nombreuses applications scientifiques, et les solveurs creux sont une étape coûteuse pour ces applications ainsi que pour des solveurs plus avancés comme les solveurs hybrides direct-itératif. Pour ces raisons, optimiser la performance de ces solveurs pour les architectures modernes est un problème critique. Cependant, les contraintes mémoire et le temps de résolution limitent l’utilisation de ce type de solveur pour des problèmes de très grande taille. Pour les approches concurrentes, par exemple les méthodes itératives, des préconditionneurs garantissant une bonne convergence pour un large ensemble de problèmes sont toujours inexistants. Dans la première partie de cette thèse, nous présentons deux approches exploitant la compression Block Low-Rank (BLR) pour réduire la consommation mémoire et/ou le temps de résolution d’un solveur creux. Ce format de compression à plat, sans hiérarchie, permet de tirer profit du caractère low-rank des blocs apparaissant dans la factorisation de systèmes linéaires creux. La solution proposée peut être utilisée soit en tant que solveur direct avec une précision réduite, soit comme un préconditionneur très robuste. La première approche, appelée Minimal Memory, illustre le meilleur gain mémoire atteignable avec la compression BLR, alors que la seconde approche, appelée Just-In-Time, est dédiée à la réduction du nombre d’opérations, et donc du temps de résolution. Dans la seconde partie, nous présentons une stratégie de reordering qui augmente la granularité des blocs pour tirer davantage profit de la localité dans l’utilisation d’architectures multi-coeurs et pour fournir de tâches plus volumineuses aux GPUs. Cette stratégie s’appuie sur la factorisation symbolique par blocs pour raffiner la numérotation produite par des outils de partitionnement comme Metis ou Scotch, et ne modifie pas le nombre d’opérations nécessaires à la résolution du problème. A partir de cette approche, nous proposons dans la troisième partie de ce manuscrit une technique de clustering low-rank qui a pour objectif de former des clusters d’inconnues au sein d’un séparateur. Nous démontrons notamment les intérêts d’une telle approche par rapport aux techniques de clustering classiquement utilisées. Ces deux stratégies ont été développées pour le format à plat BLR, mais sont également une première étape pour le passage à un format hiérarchique. Dans la dernière partie de cette thèse, nous nous intéressons à une modification de la technique de dissection emboîtée afin d’aligner les séparateurs par rapport à leur père pour obtenir des structures de données plus régulières. / Solving sparse linear systems is a problem that arises in many scientific applications, and sparse direct solvers are a time consuming and key kernel for those applications and for more advanced solvers such as hybrid direct-iterative solvers. For those reasons, optimizing their performance on modern architectures is critical. However, memory requirements and time-to-solution limit the use of direct methods for very large matrices. For other approaches, such as iterative methods, general black-box preconditioners that can ensure fast convergence for a wide range of problems are still missing. In the first part of this thesis, we present two approaches using a Block Low-Rank (BLR) compression technique to reduce the memory footprint and/or the time-to-solution of a supernodal sparse direct solver. This flat, non-hierarchical, compression method allows to take advantage of the low-rank property of the blocks appearing during the factorization of sparse linear systems. The proposed solver can be used either as a direct solver at a lower precision or as a very robust preconditioner. The first approach, called Minimal Memory, illustrates the maximum memory gain that can be obtained with the BLR compression method, while the second approach, called Just-In-Time, mainly focuses on reducing the computational complexity and thus the time-to-solution. In the second part, we present a reordering strategy that increases the block granularity to better take advantage of the locality for multicores and provide larger tasks to GPUs. This strategy relies on the block-symbolic factorization to refine the ordering produced by tools such as Metis or Scotch, but it does not impact the number of operations required to solve the problem. From this approach, we propose in the third part of this manuscript a new low-rank clustering technique that is designed to cluster unknowns within a separator to obtain the BLR partition, and demonstrate its assets with respect to widely used clustering strategies. Both reordering and clustering where designed for the flat BLR representation but are also a first step to move to hierarchical formats. We investigate in the last part of this thesis a modified nested dissection strategy that aligns separators with respect to their father to obtain more regular data structure.

Neste trabalho propomos gráficos de controle tipo CUSUM para monitoramento de tempos de sobrevivência. Nossa proposta é desenvolver diferentes estatísticas para o escore do gráfico CUSUM de forma prospectiva. Inicialmente propomos um gráfico CUSUM não paramétrico para monitoramento de populações homogêneas que avalia a variação na estatística log-rank como forma de identificar se há uma mudança significativa no risco de falha ao longo do tempo. Algumas abordagens diferentes foram consideradas e em destaque colocamos o gráfico ZDiff CUSUM, que tem como escore o incremento na estatística Z do teste log-rank em relação à inspeção anterior. Foi constatado, via simulação, que este método é eficiente. Posteriormente investigamos abordagens que levam em conta heterogeneidade na população por meio do modelo de Cox, considerando medidas baseadas na razão de verossimilhanças e em resíduos martingal e deviance. Através de simulações, verificou-se que o método com base na razão de verossimilhanças se mostrou ágil para detectar alteração na taxa de falha, quando se conhece a intensidade da mudança e este valor é informado na construção do teste. Por outro lado, os gráficos CUSUM com base em resíduos são mais simples e se mostraram eficazes para identificar aumentos no padrão da sobrevivência. Estes três métodos e o ZDiff CUSUM foram aplicados a dados de um estudo conduzido no Instituto do Coração (InCor) envolvendo pacientes com insuficiência cardíaca. Foi detectado que ao longo do tempo estes pacientes apresentam sobrevida maior, o que pode estar ligado à melhoria no tratamento e procedimentos realizados no hospital. Como conclusão, sugerimos que os gráficos tipo CUSUM com resíduos do modelo de Cox e o método não paramétrico com teste log-rank podem ser alternativas para utilização na prática em monitoramento de dados de sobrevivência. / In this work we propose CUSUM control charts to monitor survival times. Our proposal is to develop different statistics for the CUSUM chart score in a prospective way, to take into account SA approaches. We initially consider a non-parametric approach to monitor homogeneous populations. This CUSUM evaluates the variation on the log-rank test statistics as a way to identify significant changes in the risk of failure. Some different expressions for this have been considered and, in particular, we propose a ZDiff CUSUM chart computed as the increment on the log-rank test statistics Z at each inspection point in relation to the previous one. Based on simulation studies it was found that this method is efficient. Subsequently we investigated approaches that take into account heterogeneity in the population through the Cox model, considering measures based on the likelihood ratio and on martingal and deviance residuals. Through simulations, it was verified that the method based on the likelihood ratio was agile to detect a change in the hazard rate, when the intensity of the change is known and this value is informed in the construction of the test. On the other hand, CUSUM methods based on residuals are simpler and have been shown to be effective in identifying increases in survival pattern. These three methods and the ZDiff CUSUM were applied to a dataset from a study conducted at the Heart Institute (InCor) on patients with heart failure. It has been found that, over time, these patients have greater survival, which may be linked to improved treatment and procedures performed at the hospital. As a conclusion, we suggest that the CUSUM methods based on Cox model residuals and the nonparametric method on the log-rank test may be alternatives for practice in monitoring survival data.

Le récepteur activateur de NF-κB (RANK), membre de la famille des récepteurs au TNF, est connu pour son rôle dans l’homéostasie de l’os, mais joue aussi un rôle important dans le système immunitaire. J’ai tout d’abord étudié des outils permettant de cibler RANK/RANKL. J’ai caractérisé et comparé l’activité biologique de deux anticorps anti-RANK. J’ai également criblé une librairie de petites molécules pour identifier des inhibiteurs de l’interaction RANK/RANKL. Dans une deuxième partie, je me suis intéressée au rôle du ligand de RANK (RANKL) dans l’homéostasie du ganglion lymphatique. RANKL joue un rôle dans la différenciation des ostéoclastes mais son rôle dans la différenciation d’autres macrophages n’a pas été étudié. Nous avons étudié des souris déficientes pour RANKL dans les cellules marginales réticulaires (MRC) qui expriment RANKL de manière constitutive dans le ganglion adulte. Nous avons observé une diminution de la population de macrophages sous-capsulaires (SSM). Nous avons également montré que les cellules endothéliales lymphatiques (LEC) expriment l’intégrine alpha 2b (ITGA2b) et que cette expression est sensible à la présence de RANKL. / The TNF-family member Receptor Activator of NF-κB (RANK) is known for its role in bone homeostasis and is increasingly recognized as a central player in immune regulation. Firstly I looked for new molecular tools to target RANK/RANKL axis. I characterized and compared the biological activity of two anti-RANK antibodies. Moreover, I screened the Prestwick Chemical Library® of small molecules in order to identify inhibitors of RANK/RANKL interaction. Secondly, I studied the effect of the RANK/RANKL axis in lymph node homeostasis. RANKL is known to promote osteoclast differentiation but whether it also plays a role in the differentiation of other macrophage subsets is not known. We addressed this question by conditionally deleting RANKL from marginal reticular stromal cells (MRCs) that constitutively express RANKL in the lymph node. We observed impaired differentiation of the subcapsular sinus macrophages (SSMs). We also studied lymph node lymphatic endothelial cells (LECs) and showed that integrin alpha 2b (ITGA2b) is expressed by a lymph node subset of LECs and its expression is sensitive to RANKL.

The ranking method used for testing the equivalence of two distributions has been studied for decades and is widely adopted for its simplicity. However, due to the complexity of calculations, the power of the test is either estimated by normal approximation or found when an appropriate alternative is given. Here, via a Finite Markov chain imbedding (FMCI) technique, we are able to establish the marginal and joint distributions of the rank statistics considering the shift and scale parameters, respectively and simultaneously, under two continuous distribution functions. Furthermore, the procedures of distribution equivalence tests and their power functions are discussed. Numerical results of a joint distribution of two rank statistics under the standard normal distribution and the powers for a sequence of alternative normal distributions with mean from -20 to 20 and standard deviation from 1 to 9 and their reciprocals are presented. In addition, we discuss the powers of the rank statistics under the Lehmann alternatives. Wallenstein et. al. (1993, 1994) discussed power via combinatorial calculations for the scan statistic against a pulse alternative; however, unless certain proper conditions are given, computational difficulties exist. Our work extends their results and provides an alternative way to obtain the distribution of a scan statistic under various alternative conditions. An efficient and intuitive expression for the distribution as well as the power of the scan statistic are introduced via the FMCI. The numerical results of the exact power for a discrete scan statistic against various conditions are presented. Powers through the finite Markov chain imbedding method and a combinatorial algorithm for a continuous scan statistic against a pulse alternative of a higher risk for a disease on a specified subinterval time are also discussed and compared.

Η ανάπτυξη των peer-to-peer βάσεων δεδομένων και η δυναμική εισαγωγή των συστημάτων αποθήκευσης σε νέφη υπολογιστών (cloudstores) ως τα κυρίαρχα μεγάλης κλίμακας συστήματα διαχείρισης δεδομένων, έχουν οδηγήσει τους ερευνητές να εξετάσουν το πρόβλημα της υποστήριξης πολύπλοκων ερωτημάτων με ένα πλήρως αποκεντρωμένο τρόπο. Περίπλοκα ερωτήματα επιλογής (select), συνένωσης join, καθώς και βαθμολογημένα ερωτήματα έχουν κεντρίσει το ενδιαφέρον της κοινότητας διαχείρισης δεδομένων. Ανάμεσα στις τάξεις των ερωτημάτων αυτών είναι το κεντρικής σημασίας top-k join. To κατανεμημένο top-k join, δεν έχει μελετηθεί επαρκώς, αν και συναντάται πολύ συχνά σε πραγματικό φόρτο εργασίας σε πολλά εμπορικά και άλλα συστήματα βάσεων δεδομένων. Με την εργασία αυτή αντιμετωπίζουμε τέτοιου είδους ερωτήματα πάνω σε δεδομένα που είναι κατανεμημένα σε ένα μεγάλου κλίμακας δίκτυο. Οι συνεισφορές μας με αυτήν την εργασία περιλαμβάνουν: (α) ένα νέο κατανεμημένο ευρετήριο, που επιτρέπει την πρόσβαση σε πλειάδες με τυχαίο και διατεταγμένο τρόπο, (β) ένα σύνολο αλγόριθμων για βαθμολογημένα ερωτημάτατα συνένωσης join. Οι αλγόριθμοί μας στηρίζονται στην προσαρμογή γνωστών αλγοριθμών κατωφλίου για βαθμολογημένο join σε κατανεμημένο περιβάλλον, (γ) μία νέα χρήση των Bloom φίλτρων και ιστογραμμάτων για την περαιτέρω μείωση του εύρους ζώνης που καταναλώνουν οι παραπάνω αλγόριθμοι, καθώς και απόδειξη για το ότι οι αλγόριθμοί μας που βασίζονται σε φίλτρα Bloom και ιστογράμματα παράγουν το σωστό top-k αποτέλεσμα, (δ) μια σε βάθος συζήτηση του σχεδιασμού των αλγορίθμων μας και θεμάτων που συνδέονται με τις επιδόσεις και τα trade-offs. Επιπλέον διερευνούμε την αποτελεσματικότητα και την ποιότητα των προτεινόμενων λύσεων μέσα από μία αναλυτική πειραματική αξιολόγηση, δείχνοντας τις περιπτώσεις που ο κάθε αλγόριθμός μας είναι κατάλληλος σε μαζικώς κατανεμημένα και αποκεντρωμένα περιβάλλοντα, ενώ τονίζουμε τα trade-offs που προκύπτουν. / The advent of peer-to-peer databases and the recent rise of cloudstores as key large-scale data management paradigms, have led researchers to look into the problem of supporting complex queries in a fully decentralized manner. Among the classes of queries considered in related centralized work, there is one that stands out as largely overlooked in widely distributed settings, albeit very common in real-world workloads: top-k joins. With this work we tackle such queries over data distributed across an internet-scale network. Our contributions include: (a) a novel distributed indexing scheme, allowing access to tuples in both a random and an ordered manner; (b) a set of query processing algorithms based on a novel adaptation of rank-join and threshold algorithms, appropriate for use in a distributed environment; (c) a novel use of Bloom Filters and histograms to further reduce the bandwidth consumption of the above algorithms; a proof that ensures that our algorithms based on Bloom filters and histograms produce the correct top-k results; and (d) an in-depth discussion of the design space and related performance trade-offs. We further investigate the efficiency and quality of the proposed solutions through an elaborate experimental evaluation, showcasing their appropriateness for widely-distributed and massively decentralized environments and highlighting related trade-offs.

Made available in DSpace on 2014-12-17T15:32:19Z (GMT). No. of bitstreams: 1 MaiaraM_Dissert.pdf: 2968185 bytes, checksum: 105b46ac6fb81afd7b7596a11828a3c8 (MD5) Previous issue date: 2010-03-10 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / Receptor ativador nuclear κappa B (RANK), ligante do receptor ativador nuclear κappa B (RANKL) e osteoprotegerina (OPG) s?o membros da fam?lia do fator de necrose tumoral relacionados com o metabolismo ?sseo. A forma??o, diferencia??o e atividade dos osteoclastos s?o reguladas por estas tr?s prote?nas. RANK ? um receptor transmembrana presente em diversos tipos celulares, principalmente em c?lulas de linhagem macrof?gica, linf?citos, c?lulas dendr?ticas e fibroblastos e quando ativado pelo seu ligante, RANKL, promove a diferencia??o e ativa??o de c?lulas osteocl?sticas respons?veis pelo processo de reabsor??o ?ssea. A OPG impede a liga??o RANK/RANKL atuando como um receptor inibit?rio para a atividade osteol?tica. O objetivo deste estudo foi comparar a express?o imuno-histoqu?mica destes biomarcadores em cistos radiculares (n=20) e cistos dent?geros (n=20). A express?o imuno-histoqu?mica destes marcadores foi avaliada no epit?lio e na c?psula dos cistos por escores e percentuais m?dios de imunomarca??o. Para o epit?lio, a an?lise semi-quantitativa revelou um padr?o similar dos escores de imunomarca??o de RANK, RANKL e OPG nas les?es, n?o havendo diferen?a estat?stica significante (p=0.589, p=0.688, p=0.709, respectivamente). Para a c?psula c?stica a an?lise quantitativa, mostrou diferen?a estat?stica significante entre os percentuais m?dios de imunomarca??o do RANK e RANKL (p=0,001 e p=0,005, respectivamente) nos cistos. A correla??o dos escores de imunomarca??o de RANKL e OPG no epit?lio do CR e do CD revelou diferen?a estat?stica significante (p=0,029, p=0,003, respectivamente). No epit?lio dos CRs e dos CDs observou-se uma maior imunoexpress?o da OPG comparada a do RANKL. Os resultados apontam a presen?a de RANK, RANKL e OPG nos cistos radiculares e cistos dent?geros, sugerindo a atua??o destas prote?nas no desenvolvimento e expans?o das les?es no osso adjacente / Receptor ativador nuclear κappa B (RANK), ligante do receptor ativador nuclear κappa B (RANKL) e osteoprotegerina (OPG) s?o membros da fam?lia do fator de necrose tumoral relacionados com o metabolismo ?sseo. A forma??o, diferencia??o e atividade dos osteoclastos s?o reguladas por estas tr?s prote?nas. RANK ? um receptor transmembrana presente em diversos tipos celulares, principalmente em c?lulas de linhagem macrof?gica, linf?citos, c?lulas dendr?ticas e fibroblastos e quando ativado pelo seu ligante, RANKL, promove a diferencia??o e ativa??o de c?lulas osteocl?sticas respons?veis pelo processo de reabsor??o ?ssea. A OPG impede a liga??o RANK/RANKL atuando como um receptor inibit?rio para a atividade osteol?tica. O objetivo deste estudo foi comparar a express?o imuno-histoqu?mica destes biomarcadores em cistos radiculares (n=20) e cistos dent?geros (n=20). A express?o imuno-histoqu?mica destes marcadores foi avaliada no epit?lio e na c?psula dos cistos por escores e percentuais m?dios de imunomarca??o. Para o epit?lio, a an?lise semi-quantitativa revelou um padr?o similar dos escores de imunomarca??o de RANK, RANKL e OPG nas les?es, n?o havendo diferen?a estat?stica significante (p=0.589, p=0.688, p=0.709, respectivamente). Para a c?psula c?stica a an?lise quantitativa, mostrou diferen?a estat?stica significante entre os percentuais m?dios de imunomarca??o do RANK e RANKL (p=0,001 e p=0,005, respectivamente) nos cistos. A correla??o dos escores de imunomarca??o de RANKL e OPG no epit?lio do CR e do CD revelou diferen?a estat?stica significante (p=0,029, p=0,003, respectivamente). No epit?lio dos CRs e dos CDs observou-se uma maior imunoexpress?o da OPG comparada a do RANKL. Os resultados apontam a presen?a de RANK, RANKL e OPG nos cistos radiculares e cistos dent?geros, sugerindo a atua??o destas prote?nas no desenvolvimento e expans?o das les?es no osso adjacente

Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2015-03-31T12:22:43Z No. of bitstreams: 2 Dissertação - Carina Calixto Ribeiro de Araujo - 2014.pdf: 962707 bytes, checksum: 35c8b1aaf03b3f0aeefb923de0f8dfcc (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2015-04-01T10:56:06Z (GMT) No. of bitstreams: 2 Dissertação - Carina Calixto Ribeiro de Araujo - 2014.pdf: 962707 bytes, checksum: 35c8b1aaf03b3f0aeefb923de0f8dfcc (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2015-04-01T10:56:06Z (GMT). No. of bitstreams: 2 Dissertação - Carina Calixto Ribeiro de Araujo - 2014.pdf: 962707 bytes, checksum: 35c8b1aaf03b3f0aeefb923de0f8dfcc (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2014-08-29 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Information Retrieval is an area of IT that deals with document storage and the information retrieval in these documents. With the advent of the Internet, the number of documents produced has increased as well as the need to retrieve the information more accurately. Many approaches have been proposed to meet these requirements and one of them is Learning to rank (L2R). Despite major advances achieved in the accuracy of retrived documents, there is still considerable room for improvement. This master thesis proposes the use of feature selection and generation using association rules to improve the accuracy of the L2R methods. / Recuperação de Informação é a área da informática que lida com o armazenamento de documentos e a recuperação de informação desses documentos. Com o advento da internet a quantidade de documentos produzidos aumentou, bem como a necessidade de recuperar a informação de forma mais mais precisa. Muitas abordagens surgiram para suprir essa requisição e uma delas é a abordagem Learning to Rank (L2R). Apesar de obtidos grandes avanços na precisão dos documentos retornados, ainda há espaço para melhorias. Esse trabalho de mestrado propõe a utilização de seleção e geração de características utilizando regras de associação para conseguir uma melhoria na acurácia dos métodos de L2R.

We have two main results. Our first main result is a sharp bound for the number of vertices in a minimal forbidden subgraph for the graphs having minimum rank at most 3 over the finite field of order 2. We also list all 62 such minimal forbidden subgraphs and show that many of these are minimal forbidden subgraphs for any field. Our second main result is a structural characterization of all graphs having minimum rank at most k for any k over any finite field. This characterization leads to a very strong connection to projective geometry and we apply projective geometry results to the minimum rank problem.

No description available.

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]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/104923