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

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:237

Article

Roman, J. E.¹  Vasconcelos, P. B.^2,3  Nunes, A. L.⁴ 

[1] Univ Politecn Valencia, D Sistemes Informat & Computacio, E-46022 Valencia, Spain

[2] Univ Porto, Ctr Matemat, P-4200464 Oporto, Portugal

[3] Univ Porto, Fac Econ, P-4200464 Oporto, Portugal

[4] Inst Politecn Cavado & Ave, P-4750333 Barcelos, Portugal

关键词: Iterative eigensolvers;    Integral operator;    Hierarchical matrices;    Numerical libraries;   

DOI  :  10.1016/j.cam.2012.07.021

来源: Elsevier

【 摘 要 】

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. (C) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

Free