Banca de QUALIFICAÇÃO: JOSIMARA TATIANE DA SILVA

Uma banca de QUALIFICAÇÃO de MESTRADO foi cadastrada pelo programa.
DISCENTE : JOSIMARA TATIANE DA SILVA
DATA : 25/05/2016
HORA: 09:30
LOCAL: Sala de seminários de estatística CCET
TÍTULO:

Preconditioning of the GMRES($m$) method for special classes

PALAVRAS-CHAVES:

Z-matrices, Krylov Methods, Convergence of GMRES($m$), $ILU(0)$ Preconditioner.

PÁGINAS: 62
GRANDE ÁREA: Ciências Exatas e da Terra
ÁREA: Matemática
SUBÁREA: Matemática Aplicada
ESPECIALIDADE: Análise Numérica
RESUMO:

This study aims to investigate the convergence behavior of GMRES($m$) (Generalized Minimal Residual) method
with and without preconditioner ILU$(0)$ applied to large sparse non-symmetric linear systems. Based already on the
numerical stability of the incomplete $LU$ factorization for special classes of matrices, namely, the $M$-matrizes and
the $H$-matrices, we study situations where the coefficient matrix belongs to a less restricted class than these ---
the $Z$-matrizes. Then we generate matrices, denoted by $K$-matrizes, written as linear combinations of two
$Z$-matrizes, which do not belong to this class. It is expected that the GMRES($m$) preconditioned with $ILU(0)$
to have a better performance (less CPU time of execution, number of iterations, residual norm) for $Z$-matrizes
than for $K$-matrizes knowing, \textit{a priori}, the stability of such decomposition. We compare the performance of the GMRES($m$)
with preconditioned GMRES($m$). We also evaluate the influence of the degree of sparsity of these matrices with the
results of the GMRES($m$). Numerical experiments were carried out to confirm possible relations.

MEMBROS DA BANCA:
Interno - 1958710 - EDGAR SILVA PEREIRA
Externo ao Programa - 1679134 - JULIA VICTORIA TOLEDO BENAVIDES
Presidente - 1703737 - NIR COHEN