Eigenvalue computations in the context of data-sparse approximations of integral operators

Authors:
J. E. Roman;P. B. Vasconcelos;A. L. Nunes
Affiliations:
D. Sistemes Informítics i Computació, Universitat Politècnica de València, Camí de Vera s/n, E-46022 València, Spain;Centro de Matemática, and Faculdade Economia, Universidade Porto, R. Dr. Roberto Frias s/n, P-4200-464 Porto, Portugal;Instituto Politécnico do Cávado e do Ave, Av. Dr. Sidónio Pais 222, P-4750-333 Barcelos, Portugal
Venue:
Journal of Computational and Applied Mathematics
Year:
2013

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Abstract

In this work, we consider the numerical solution of a large eigenvalue problem resulting from a finite rank discretization of an integral operator. We are interested in computing a few eigenpairs, with an iterative method, so a matrix representation that allows for fast matrix-vector products is required. Hierarchical matrices are appropriate for this setting, and also provide cheap LU decompositions required in the spectral transformation technique. We illustrate the use of freely available software tools to address the problem, in particular SLEPc for the eigensolvers and HLib for the construction of H-matrices. The numerical tests are performed using an astrophysics application. Results show the benefits of the data-sparse representation compared to standard storage schemes, in terms of computational cost as well as memory requirements.