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Seminario: On the convergence of Krylov methods for solving non symmetric linear

Tuesday, April 29, 2014, h. 13:00 - Room 2BC30 - Gérard Meurant

ARGOMENTI: Seminari

Tuesday, April 29, 2014, h. 13:00 - Room 2BC30
"On the convergence of Krylov methods for solving non symmetric linear systems"
Gérard Meurant (Former Research Director, Commissariat à l'Energie Atomique, France)

Abstract
Today Krylov methods are the most popular iterative methods for solving linear systems. In this talk we consider their residual norms and their decrease. We will recall what are the known results for GMRES (Generalized Minimum Residual method) and we will show how to obtain exact expressions for the residual norms for diagonalizable matrices. They involve the eigenvalues and eigenvectors of the matrix as well as the right-hand side.
To a certain extent they allow to explain the good or bad convergence of the method. Then we will study how to extend some of these results to other Krylov methods like the biconjugate gradient or the QMR method.

Short CV
Gérard Meurant studied in Paris XI University (Orsay) where he got his degree in numerical analysis in 1972 under the supervision of R. Temam. From 1973 to 2008 he worked for the French "Commissariat à l'énergie atomique". During most of these years he was in charge of supervising the development of simulation codes and their adaptation to new computer architectures for solving different problems from physics. One of his major interest was parallel computing and parallelization of numerical methods. His last position when he retired in 2008 was Directeur de Recherches. His main research topic is solving linear systems of equations using iterative methods and the estimation of errors for the related algorithms. He published many papers on these topics as well as four books. The last one published in 2010 is devoted to the computation of estimates of quadratic forms with applications to several problems in numerical computations.