Naslov
Increasing efficiency of inverse iteration

Autori
Bosner, Nela

Izvornik
Annali dell'Università di Ferrara. Sezione 7: Scienze matematiche (1827-1510) 54 (2008), 2; 203-216

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
eigenvalue problem ; inverse iteration ; multigrid methods

Sažetak
Inverse iteration is simple but not very efficient method for computing few eigenvalues with minimal absolute values and corresponding eigenvectors of a symmetric matrix. The idea is to increase its efficiency by technique similar to multigrid methods used for solving linear systems. This approach is not new, but until now multigrid was mostly used for solving linear system which appear in Rayleigh quotient iteration, inverse iteration and related iterative methods. Instead of choosing appropriate coordinates (grids), our algorithm performs inverse iteration on a sequence of subspaces with decreasing dimensions (multispace). Block Lanczos method is used for the selection of a smaller subspace. This will produce a banded matrix, which makes inverse iteration even faster in the smaller dimensions.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA