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Un esquema paralelo para el cálculo del pseudoespectro de matrices de gran magnitud;
A parallelizable scheme for pseudospectra computing of large matrices
Otero Calviño, Beatriz; Astudillo, Reinaldo; Castillo, Zenaida
Universitat Politècnica de Catalunya. Departament d'Arquitectura de Computadors; Universitat Politècnica de Catalunya. CAP - Grup de Computació d´Altes Prestacions
The pseudospectra is a powerful tool to study the behavior of dynamic systems associated to non-normalmatrices. Studies and applications have increased in the last decades, thus, its efficient computation hasbecome of interest for the scientific community. In the large scale setting, different approaches have beenproposed, some of them based on projection on Krylov subspaces. In this work we use the idea proposed byWright and Trefethen to approximate the pseudospectra of a matrix A using a projection Hmof smallersize. Additionally, we propose a domain decomposition of the interest region into subregions whichare assigned to a set of processors. Each processor calculates the minimal singular values of matrices(zI - Hm) where z = x + yi represents a point of the corresponding subregion. We conduct a numericalexperimentation comparing the results with those on the literature of the topic. In all cases the proposedscheme shows a reduction in CPU time with respect to the sequential version, achieving from 41x to 101x.
Peer Reviewed
Àrees temàtiques de la UPC::Informàtica::Arquitectura de computadors::Arquitectures paral·leles
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes numèrics
Parallel processing (Electronic computers)
Iterative methods (Mathematics)
Pseudospectra
Krylov methods
Projection
Data parallelism
Processament en paral·lel (Ordinadors)
Mètodes iteratius (Matemàtica)
info:eu-repo/semantics/submittedVersion
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