TY - GEN A1 - Mackey, D. Steven A1 - Mackey, Niloufer A1 - Mehl, Christian A1 - Mehrmann, Volker T1 - Numerical methods for palindromic eigenvalue problems: Computing the anti-triangular Schur form N2 - We present structure-preserving numerical methods for complex palindromic polynomial eigenvalue problems via corresponding palindromic linearizations. A key ingredient is the development of an appropriate condensed form --- the anti-triangular Schur form. Ill-conditioned problems which have eigenvalues near the unit circle, in particular near +/-1, are discussed. We show how a combination of unstructured methods followed by a structured refinement can be used to solve such problems very accurately. KW - nonlinear eigenvalue problem KW - palindromic KW - matrix polynomial KW - Schur form KW - anti-triangular form KW - Jacobi algorithm KW - structured deflation method KW - palindromic QR-algorithm Y1 - 2007 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/413 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-4135 ER -