Papers by Danny Joel Guerrero Flores
In this compilation, the logistic model and the SIR model are tested to forecast the spread of Co... more In this compilation, the logistic model and the SIR model are tested to forecast the spread of Covid-19 virus in Honduras by using the software Matlab. The mathematics topics involved are presented in a friendly way to facilitate their reading and to identify some possible didactic practices derived from their application. Certainly, some graphs, data arrangements and comments about the results obtained are given. The forecasts in this document depended on the handling of the data provided by the Hondurean's authorities.
The main topic of this thesis is updating preconditioners for solving large sparse linear systems... more 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 nonsingular, non-symmetric linear systems where the coefficient matrix A has a skewsymmetric 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. To my family. A special feeling of gratitude to my wife Elisa Savoia and my daughter Lucía Guerrero. I also dedicate this thesis to my friends who have supported me throughout the process. To each professor I had during my education, in particular, my project coordinators José Marín, José Mas and Juana Cerdán who have been more than generous with their expertise and precious time spent with me for preparing this thesis. To the
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Papers by Danny Joel Guerrero Flores