TY - GEN A1 - Schröder, Christian T1 - A QR-LIKE ALGORITHM FOR THE PALINDROMIC EIGENVALUE PROBLEM N2 - 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. KW - palindromic eigenvalue problem KW - QR algorithm KW - unitary congruence KW - canonical form KW - Hessenberg matrix Y1 - 2007 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/392 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-3921 ER -