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Seminar

des DFG-Sonderforschungsbereichs 393

Numerische Simulation auf massiv parallelen Rechnern


Zeit: Donnerstag, 11.11.1999, 17:00 Uhr
Ort: Reichenhainer Straße 70, B202
Vortragender: P. Tichy (Prag)
Thema: The shadow vector in the Lanczos method
Lanczos method for solving the system of linear algebraic equations Ax=b consists in constructing a sequence of vectors xk in such a way that
$r_k=b-Ax_k \in r_0+A{\cal K}_k(A,r_0)$

and
$r_k \perp {\cal K}_k(A^T,\widetilde{r}_0)$

where $\widetilde{r}_0$ is an auxiliary vector often called the shadow vector.
It will be shown that, by the choice of shadow vector, it is possible, in certain sense, to make the Lanczos method to be closer to some other Krylov subspace method (KSM) like GMRES, and that almost every three-term KSM can be implemented by the Lanczos method within first [n/2] iterations where n is the rank of the matrix A.
Das Seminar wird von Herrn Prof. Mehrmann geleitet. Interessenten sind herzlich eingeladen.

Thomas Apel,