BIT Numerical Mathematics

, Volume 54, Issue 1, pp 189–200 | Cite as

A bisection method for measuring the distance of a quadratic matrix polynomial to the quadratic matrix polynomials that are singular on the unit circle

  • Alexander Malyshev
  • Miloud Sadkane


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.


Distance to instability Quadratic matrix polynomial Bisection algorithm Level set algorithm Error analysis 

Mathematics Subject Classification (2010)

15A22 93B35 



The authors thank the referees for making useful remarks and suggestions on the manuscript.


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of BergenBergenNorway
  2. 2.CNRS-UMR 6205, Laboratoire de Mathématiques de Bretagne AtlantiqueUniversité de BrestBrest Cedex 3France

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