• search hit 17 of 24
Back to Result List

A QR-LIKE ALGORITHM FOR THE PALINDROMIC EIGENVALUE PROBLEM

Please always quote using this URN:urn:nbn:de:0296-matheon-3921
  • In this paper we develop a QR-like algorithm for the palindromic eigenvalue problem $Ax=\lambda A^\adj x$. We will discuss the two cases that $A^\adj$ denotes the transpose or the conjugate transpose of $A\in\C^{n,n}$. It is shown that this so-called palindromic QR iteration is equivalent to applying the standard QR algorithm to $A^{-\adj}A$. Also the concepts of deflation, shifting, and exploiting the invariance of a Hessenberg-type form are adapted. Moreover, we analyze the problem of reducing a general square matrix to the mentioned Hessenberg-type form and establish analogies to the Hamiltonian eigenvalue problem. Finally, we present concrete Hessenberg-type reduction algorithms for special cases.

Download full text files

Export metadata

Additional Services

Share in Twitter Search Google Scholar
Metadaten
Author:Christian Schröder
URN:urn:nbn:de:0296-matheon-3921
Referee:Volker Mehrmann
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2007/05/23
Release Date:2007/05/23
Tag:
Institute:Technische Universität Berlin
MSC-Classification:15-XX LINEAR AND MULTILINEAR ALGEBRA; MATRIX THEORY / 15Axx Basic linear algebra / 15A18 Eigenvalues, singular values, and eigenvectors
15-XX LINEAR AND MULTILINEAR ALGEBRA; MATRIX THEORY / 15Axx Basic linear algebra / 15A21 Canonical forms, reductions, classification
15-XX LINEAR AND MULTILINEAR ALGEBRA; MATRIX THEORY / 15Axx Basic linear algebra / 15A22 Matrix pencils [See also 47A56]
15-XX LINEAR AND MULTILINEAR ALGEBRA; MATRIX THEORY / 15Axx Basic linear algebra / 15A23 Factorization of matrices
65-XX NUMERICAL ANALYSIS / 65Fxx Numerical linear algebra / 65F15 Eigenvalues, eigenvectors
Preprint Number:388
Verstanden ✔
Diese Webseite verwendet technisch erforderliche Session-Cookies. Durch die weitere Nutzung der Webseite stimmen Sie diesem zu. Unsere Datenschutzerklärung finden Sie hier.