TY - GEN A1 - Kressner, Daniel A1 - Schröder, Christian A1 - Watkins, David S. T1 - Implicit QR Algorithms for Palindromic and Even Eigenvalue Problems N2 - In the spirit of the Hamiltonian QR algorithm and other bidirectional chasing algorithms, a structure-preserving variant of the implicit QR algorithm for palindromic eigenvalue problems is proposed. This new palindromic QR algorithm is strongly backward stable and requires less operations than the standard QZ algorithm, but is restricted to matrix classes where a preliminary reduction to structured Hessenberg form can be performed. By an extension of the implicit Q theorem, the palindromic QR algorithm is shown to be equivalent to a previously developed explicit version. Also, the classical convergence theory for the QR algorithm can be extended to prove local quadratic convergence. We briefly demonstrate how even eigenvalue problems can be addressed by similar techniques. KW - palindromic eigenvalue problem KW - implicit QR algorithm KW - bulge chasing KW - bulge exchange KW - (even eigenvalue problem KW - convergence theory) Y1 - 2008 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/449 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-4493 ER -