Naslov
Second order Krylov Schur algorithm with arbitrary filter

Autori
Šain Glibić, Ivana

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, neobjavljeni rad, znanstveni

Skup
6th Croatian Mathematical Congress

Mjesto i datum
Zagreb, Hrvatska, 14.06.2016. - 17.06.2016

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Nije recenziran

Ključne riječi
eigenvalues, quadratic eigenvalue problem, Krylov subspace, Arnoldi algorithm, filter, scaling
(eigenvalues ; quadratic eigenvalue problem ; Arnoldi algorithm ; Krylov subspace ; filter ; scaling)

Sažetak
One way of solving quadratic eigenvalue problem (QEP) is to linearize it and use well known techniques to solve linear eigenproblem. However, eigenvalue properties are not preserved due to the fact that linearization does not preserve structural properties of original problem. Hence, we need methods which are applied to the QEP directly. Bai and Su defined second order Krylov subspace, and second order Arnoldi procedure for generating an orthonormal basis for the subspace. By applying Rayleigh - Ritz orthogonal projection they derived an SOAR method for solving large QEPs. Jia and Sun then introduced generalized second order Arnoldi method (GSOAR) which allows implicit restarting just like in IRAM (Implicitly restarted Arnoldi method). In our talk we propose second order Krylov Schur method which is inspired by Krylov Schur method for linear problem and SOAR method for QEP. As in IRAM, implicitly restarted GSOAR has difficulties with preserving the structure of the decomposition. We define second order Krylov decomposition which has no structure constraints. This makes restarting the method easier. The choice of shifts for QEP is delicate issue, which is why our algorithm can use arbitrary filter while restarting. We also discuss influence of eigenvalue parameter scaling on convergence of our method.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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