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Some software tools to control the accuracy in scientific computing

Jean-François Carpraux 1
1 ALADIN - Algorithms Adapted to Intensive Numerical Computing
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, INRIA Rennes
Abstract : A main concern of scientific computing is the validation of numerical simulations. Indeed, several factors contribute to the degradation of accuracy in the final result. This thesis deals with new tools to control the accuracy for the following eigenproblem~: Problem $(P)$~: \it Given $A \in \mbox\ens C^n \times n$, find some $\lambda \in \mbox\ens C$ and/or $x \in \mbox\ens C^n$ such that~: $\lambda$ is an eigenvalue of $A$ and $x$ is the associated eigenvector. We present in the first part of this thesis an expert system called SESAME, which can either select the sequence of LAPACK routines solving the given problem $(P)$ or validate a user choice of routines. It can eventually give an estimation of the accuracy of the result. The spectral portrait of a matrix provides useful informations about it. Usually, the spectral portrait is computed using a Singular Value Decomposition, but this approach is not suitable for large sparse matrices. The second part of the thesis is devoted to the computation of the spectral portrait for large sparse matrices. Krylov subspaces have an important place in sparse linear algebra, since numerous iterative methods in linear algebra dealing with large sparse matrices require these subspaces. In the third part of the thesis, we study theoretically the condition number of Krylov bases and subspaces.
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Submitted on : Wednesday, May 24, 2006 - 2:59:51 PM
Last modification on : Friday, February 4, 2022 - 3:23:45 AM
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  • HAL Id : inria-00074295, version 1


Jean-François Carpraux. Some software tools to control the accuracy in scientific computing. [Research Report] RR-2382, INRIA. 1994. ⟨inria-00074295⟩



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