Naslov
On Accuracy Of Hierarchical Rayleigh-Ritz Methods

Autori
Grubišić, Luka

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Skup
Young Researcher's Minisymposium: `` Iterative methods for large and structured matrix computations'' at the 77th Annual Meeting of the Gesellschaft für Angewandte Mathematik und Mechanik e.V.

Mjesto i datum
Njemačka, 27.03.2006. - 31.03.2006

Vrsta sudjelovanja
Pozvano predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Ritz value; Ritz vector; Finite elements

Sažetak
We present an analysis of the accuracy of hierarchical(adapted) finite element Rayleigh– Ritz method for elliptic self-adjoint eigenvalue problems. The celebrated Wilkinson’ s Schur complement trick is adapted and applied to yield a new class of Temple-Kato like inequalities which are particularly suited to a situation in which we are estimating a multiple eigenvalue (of an elliptic self-adjoint operator) by a cluster of Ritz values. The new approximation estimates are combined with Doerfler and Nochetto’ s analysis of the saturation assumption (cf. Numer. Math., 91(1)) to obtain a detailed analysis of the (preconditioned) residual approximation measure of Neymeyr (cf. Numer. Linear Algebra Appl., 9(4)). We also show how to adapt this estimation method to a situation when one is approximating a cluster of eigenvalues. New eigenvector and invariant subspace approximation estimates, in which the same (preconditioned) residual measure features, accompany the eigenvalue results. Numerical experiments, illustrating the theory, will also be presented.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA