Session B7 - Numerical Linear Algebra
July 14, 14:30 ~ 15:00
Revisiting the perfect shift strategy
Paul Van Dooren
Catholic University of Louvain, Belgium - firstname.lastname@example.org
In this paper we revisit the problem of performing a QR-step on an unreduced Hessenberg matrix when we know an exact eigenvalue of this matrix. Under exact arithmetic, this eigenvalue will appear on diagonal of the transformed Hessenberg matrix and will be decoupled from the remaining part of the Hessenberg matrix, thus resulting in a deflation. But it is well known that in finite precision arithmetic the so-called perfect shift gets blurred and the eigenvalue can not be deflated and/or is perturbed significantly. In this paper, we develop a new strategy for computing such a QR step so that the deflation is always successful.
Joint work with Nicola Mastronardi (CNR Bari, Italy).