Naslov
Relative eigenvalue/eigenvector estimates for multi-scale problems in science and engineering

Autori
Grubišić, Luka ; Drmač, Zlatko ; Kostrykin, Vadim ; Veselić, Krešimir

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

Skup
13th ILAS conference

Mjesto i datum
Amsterdam, Nizozemska, 18.07.2006. - 21.07.2006

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
relative perturbation thory ; multi-scale problems

Sažetak
We consider the eigenvalue/eigenvector approximation problem for matrices which originate as discretizations of the problems of the Large Coupling Limit, Our aim is to obtain estimates which correctly adapt to the singularities which a discretisation inherits. On the model problems we consider, known sin(Theta) theories (Davis– Kahan, Ipsen, Li, Mathias– Veselic...) give only a partial answer since they sometimes fail to resolve the singularity which the coupling introduces into the eigenvalue problem. We reconsider the approximation problem in the geometry of the ``energy'' norm. The obtained estimates are an energy norm variant of the Mathias– Veselic eigenvector inequalities. A new class of cluster robust quadratic estimates for eigenvalues will also be presented. They improve the quadratic relative-residual estimates of Drmac and Hari. We also show that on our model problems new eigenvalue inequalities outperform estimates which are functions of the absolute residuum and the absolute gap. At the end, as an alternative to a sin (Theta)-approach for obtaining invariant subspace estimates we present a relative version of the tan 2(Theta) theory. These results have been obtained through a study of the weakly formulated Riccati equation and are considerably sharper than the previously known ``relative'' sin(Theta) inequalities. Numerical experiments which corroborate the theory will be presented.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA