Computação verificada aplicada à resolução de sistemas lineares intervalares densos em arquiteturas multicore

• Ano de defesa: 2010
• Autor(a) principal: Milani, Cleber Roberto
• Orientador(a): Fernandes, Luiz Gustavo Leão
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Pontifícia Universidade Católica do Rio Grande do Sul; Porto Alegre
• Palavras-chave em Português: INFORMÁTICA; MATEMÁTICA COMPUTACIONAL; SISTEMAS LINEARES; PROCESSAMENTO PARALELO; ARQUITETURA DE COMPUTADOR
• Link de acesso: http://hdl.handle.net/10923/1477

Bounding the solution set of Systems of Linear Equations is a major problem in Computer Science. However, traditional methods offer no guarantee of correct solutions and not even of the existence of a solution. Hence, automatic result verification is an important additional tool in these algorithms. However, Verified Computing increases the computational cost and, in some cases, the required resolution time becomes unacceptable. The use of High Performance Computing (HPC) techniques appears as a solution. Several works have focused on optimizing Verified Computing performance for computer clusters. However, many changes have been occurring in High Performance Computing. Given the number of cores on multicore chips expected to reach tens in a few years, efficient implementations of numerical solutions using shared memory programming models is of urgent interest. In this context, this work presents a self-verified solver for Dense Interval Linear Systems optimized for parallel execution on multicores processors. The adopted strategies have resulted in a scalable solver that obtained up to 85% of reduction at execution time and a speedup of 6. 70 when solving a 15,000x15,000 Interval Linear System on a eight core computer.