Introducció a l'àlgebra lineal numèrica en paral·lel

Abstract

[en] Nowadays, the technological advances give us the possibility to use computers that are capable to do several tasks and, in addition, they are approachable for a lot of people. Moreover, the Numerical Linear Algebra is full of problems that require a high calculation power and adapting them to actual technology is essential to gain efficiency and time. The main purpose of this research is to remember the numerical methods studied at the Degree in Mathematics, analyzing the possible implicit parallelisms, if there are any, and to take profit of them in order to create parallel implementations. First of all, we will study the basic operational system of a computer that is capable of working in parallel and the we will study too the OpenMP programming language. Then, we will study which parallelisms we can find in classical methods and we will apply them in OpenMP language. Finally, we will see some alternative methods of solving linear systems, like the Conjugate Gradient method or the Cyclic Reduction method, analyzing also the parallelisms that may exist.