Convergence of Multipower Defect-Correction for spectral computations of integral operators

• Type: Article in International Scientific Journal
• Date: 2012

Authors

dalmeida, fd (Author) FEUP; vasconcelos, pb (Author) FEP

Journal

Title: Applied Mathematics and Computation

Vol. 219 No. 4

Pages: 1601-1606

ISSN: 0096-3003

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 1 Citation

ISI Web of Science

Scopus - 1 Citation

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-002-416

DOI: 10.1016/j.amc.2012.08.001

Abstract (EN): In this paper we propose the Multipower Defect-Correction method, a generalization of the double iteration, to compute a cluster of eigenvalues and the associated invariant subspace from discretized integral operators. It consists of an inner/outer iteration where, inside a defect-correction iteration, p power iteration steps are performed. The approximate inverse used in the defect correction is built with an approximation to the reduced resolvent operator of a coarse discretization of the integral operator. The proposed method computes eigenpairs approximations by refining initial approximations obtained from a coarser dimensional problem. It is therefore meant for large dimensional problems. Furthermore, the kernel of the integral operator may be weakly singular. We provide a proof for the convergence of this Multipower Defect-Correction method. A numerical example illustrating the theory and the behavior of the method is also presented.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 6