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Perturbation Bounds for the Nonlinear Matrix Equation Open image in new window

  • Ivan Popchev
  • Petko Petkov
  • Mihail Konstantinov
  • Vera Angelova
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7116)

Abstract

In this paper we make a complete perturbation analysis of the nonlinear matrix equation Open image in new window , where A and B are square complex matrices, Open image in new window denotes the complex conjugate transpose of the matrix A and I is the identity matrix. We obtain local (first order) perturbation bounds and a non-local perturbation bound for the solution to the equation. The perturbation bounds allow to derive condition and accuracy estimates for the computed solution, when using a stable numerical algorithm to solve the equation.

Keywords

perturbation analysis nonlinear matrix equations condition numbers perturbation bounds Lyapunov majorants 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Ivan Popchev
    • 1
  • Petko Petkov
    • 2
  • Mihail Konstantinov
    • 3
  • Vera Angelova
    • 1
  1. 1.Institute of Information and Communication TechnologiesBulgarian Academy of SciencesSofiaBulgaria
  2. 2.Department of AutomaticsTechnical University of SofiaSofiaBulgaria
  3. 3.Civil Engineering and GeodesyUniversity of ArchitectureSofiaBulgaria

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