Naslov
Extracting spectral information from large "singularly perturbed" matrices

Autori
Grubišić, Luka

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

Skup
Joint GAMM-SIAM Conference on Applied Linear AlgebraJoint GAMM-SIAM Conference on Applied Linear Algebra

Mjesto i datum
Düsseldorf, Njemačka, 24.07.2006. - 27.07.2006

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
singular perturbations ; large matrix eigenvalue problems

Sažetak
We discuss how to design a mesh refinement procedures for singularly perturbed eigenvalue problems. We are interested in methods which produce a hierarchical sequence of matrices whose eigenvectors will be progressively better resolved by the underlying triangulation. As a measure of the agreement between a triangulation and an approximate eigenvector we use the osc-function of Morin, Nochetto and Siebert. We argue that for our class of ``discretization'' matrices the (realistic) residuum should reflect both the algebraic and the analytic properties of the approximate eigenvector (equally for a more general invariant subspace setting). Numerical examples which illustrate the theory will also be presented. Typical matrices of interest have their origin (or better to say their singularities have) in problems of the Large Coupling Limit (in both Quantum and Classical Mechanics) or can be seen as Laplace matrices of weighted graphs where the weights of some edges tend to explode. Acknowledgement : Some of the results are a product of a joint work with Prof. Kre.simir Veselic, Hagen and Prof. Zlatko Drmac, Zagreb.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA