Resolució de sistemes d’equacions lineals de dimensió gran

Abstract

The present study pretends to present some iterative methods to solve systems of equations of large dimension and sparse matrices. It also tries to be a brief introduction to parallel programming world, particularly in OpenMP, a set of directives which extend Fortran and C so that different cores of the same computer can cooperate within a single program. The work has been divided into three parts. Chapter one explains theoretical basis of the methods: Jacobi, Gauss-Seidel, SOR, Conjugate Gradient, Preconditioned Conjugated Gradient and GMRES. Chapter two presents an introduction to parallel programming, a brief summary of its historty and an introduction to OpenMP and how it can be used for parallel programming. Chapter three explains how to parallelize the methods presented in chapter one and their performance. The performance has been studied by comparing the same algorithm runned with diverse threads and not between the diverse algorithms, because it would make no sense if it is not referred to a specific system of equations.