Title: An implicit Q-theorem for Hessenberg-like matrices
Authors: Vandebril, Raf
Van Barel, Marc
Mastronardi, Nicola
Issue Date: Jun-2004
Publisher: Department of Computer Science, K.U.Leuven, Leuven, Belgium
Series Title: TW Reports vol:TW394
Abstract: The implicit Q-theorem for Hessenberg matrices is a widespread
and powerful theorem. It is used in the development of for example implicit QR-algorithms to compute the eigendecomposition
of Hessenberg matrices. Moreover it can also be used to prove the essential uniqueness of orthogonal similarity transformations of
matrices to Hessenberg form. The theorem is also valid for symmetric tridiagonal matrices, proving thereby also in the symmetric case
its power.
Currently there is a growing interest to so-called semiseparable
matrices. These matrices can be considered as the inverses of tridiagonal matrices. In a similar way, one can consider Hessenberg-like matrices as the inverses of Hessenberg matrices.
In this paper, we formulate and prove an implicit Q-theorem for Hessenberg-like matrices. Similarly, like in the Hessenberg case the notion of unreduced Hessenberg-like matrices is introduced and also a method for transforming matrices via orthogonal transformations to this form is proposed. Moreover, as the theorem is valid for Hessenberg-like matrices it is also valid for symmetric semiseparable
Publication status: published
KU Leuven publication type: IR
Appears in Collections:Numerical Analysis and Applied Mathematics Section
Electrical Engineering - miscellaneous

Files in This Item:
File Status SizeFormat
TW394.pdf Submitted 193KbAdobe PDFView/Open


All items in Lirias are protected by copyright, with all rights reserved.