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Perturbation Bounds for the Nonlinear Matrix Equation

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Large-Scale Scientific Computing (LSSC 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7116))

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Abstract

In this paper we make a complete perturbation analysis of the nonlinear matrix equation , where A and B are square complex matrices, 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.

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References

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Author information

Authors and Affiliations

  1. Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, 1113, Sofia, Bulgaria

    Ivan Popchev & Vera Angelova

  2. Department of Automatics, Technical University of Sofia, 1756, Sofia, Bulgaria

    Petko Petkov

  3. Civil Engineering and Geodesy, University of Architecture, 1046, Sofia, Bulgaria

    Mihail Konstantinov

Authors
  1. Ivan Popchev
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  2. Petko Petkov
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  3. Mihail Konstantinov
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  4. Vera Angelova
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Editor information

Editors and Affiliations

  1. Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Acad. G. Bonchev, Block 25A, 1113, Sofia, Bulgaria

    Ivan Lirkov  & Svetozar Margenov  & 

  2. Department of Informatics and Mathematical Modelling, Technical University of Denmark, Richard Petersens Plads, Building 321,, 2800, Kongens Lyngby, Denmark

    Jerzy Waśniewski

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© 2012 Springer-Verlag Berlin Heidelberg

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Popchev, I., Petkov, P., Konstantinov, M., Angelova, V. (2012). Perturbation Bounds for the Nonlinear Matrix Equation . In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2011. Lecture Notes in Computer Science, vol 7116. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29843-1_17

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  • DOI: https://doi.org/10.1007/978-3-642-29843-1_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-29842-4

  • Online ISBN: 978-3-642-29843-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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