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First Order Eigenvalue Perturbation Theory and the Newton Diagram

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Applied Mathematics and Scientific Computing

Abstract

First order perturbation theory for eigenvalues of arbitrary matrices is systematically developed in all its generality with the aid of the Newton diagram, an elementary geometric construction first proposed by Isaac Newton. In its simplest form, a square matrix A with known Jordan canonical form is linearly perturbed to A(ε) = A + ε B for an arbitrary perturbation matrix B, and one is interested in the leading term in the ε-expansion of the eigenvalues of A(ε). The perturbation of singular values and of generalized eigenvalues is also covered.

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Authors and Affiliations

  1. Departamento de Matematicás, Universidad Carlos III de Madrid, Spain

    Julio Moro & Froilán M. Dopico

Authors
  1. Julio Moro
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  2. Froilán M. Dopico
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Editor information

Editors and Affiliations

  1. University of Zagreb, Zagreb, Croatia

    Zlatko Drmač , Vjeran Hari  & Zvonimir Tutek ,  & 

  2. University of Rijeka, Rijeka, Croatia

    Luka Sopta

  3. University of Hagen, Hagen, Germany

    Krešimir Veselić

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Moro, J., Dopico, F.M. (2002). First Order Eigenvalue Perturbation Theory and the Newton Diagram. In: Drmač, Z., Hari, V., Sopta, L., Tutek, Z., Veselić, K. (eds) Applied Mathematics and Scientific Computing. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-4532-0_6

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  • DOI: https://doi.org/10.1007/978-1-4757-4532-0_6

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4419-3390-4

  • Online ISBN: 978-1-4757-4532-0

  • eBook Packages: Springer Book Archive

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