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A bisection method for measuring the distance of a quadratic matrix polynomial to the quadratic matrix polynomials that are singular on the unit circle |
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| Authors: | Alexander Malyshev Miloud Sadkane |
| Institution: | 1. Department of Mathematics, University of Bergen, Postbox 7800, 5020, Bergen, Norway 2. CNRS-UMR 6205, Laboratoire de Mathématiques de Bretagne Atlantique, Université de Brest, 6, Av. Le Gorgeu, 29238, Brest Cedex 3, France |
| Abstract: | The computation of the distance of a quadratic matrix polynomial to the quadratic matrix polynomials that are singular on the unit circle is investigated. The emphasis is placed on backward stable methods that transform the computation of the distance to a palindromic eigenvalue problem for which structure-preserving eigensolvers can be utilized in conjunction with a bisection algorithm. Reliability of the suggested methods is guaranteed by a novel error analysis. |
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