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Perturbation analysis of eigenvalues of polynomial matrices smoothly depending on parameters

Authors:

M. Isabel García-Planas,

Sonia TarragonaAuthors Info & Claims

Proceedings of the 15th WSEAS international conference on Systems

Pages 100 - 105

Published: 14 July 2011 Publication History

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Abstract

Let P(λ) = Σ_i=0^kλⁱA_i(p) be a family of monic polynomial matrices smoothly dependent on a vector of real parameters p = (p₁,..., p_n). In this work we study behavior of a multiple eigenvalue of the monic polynomial family P(λ).

References

[1]

A.L. Andrew, K.-W. E. Chu, P. Lancaster, Derivatives of eigenvalues and eigenvectors of matrix functions, SIAM journal on matrix analysis and applications, 14, (4), pp. 903-926, (1993).

Digital Library

Google Scholar

[2]

P. Benner, V. Mehrmann, H. Xu, Perturbation Analysis for the Eigenvalue Problem of a Formal Product of Matrices, BIT, Numerical Mathematics, 42, pp. 1-43, (2002).

Crossref

Google Scholar

[3]

E. King-Wah Chu, Perturbation of eigenvalues for matrix polynomials via the Bauer-Fike Theorems, SIAM journal on matrix analysis and applications, 25, (2), pp. 551-573, (2004).

Digital Library

Google Scholar

[4]

M. I. García, Introducción a la Teoría de Matrices Polinomiales. Edicions UPC, Barcelona, 1999.

Google Scholar

[5]

M. I. García-Planas, Kronecker Stratification of the Space of Quadruples of Matrices. SIAM Journal on Matrix Analysis 19 (4), pp. 872-885, (1998).

Digital Library

Google Scholar

[6]

M. I. García-Planas, S. Tarragona, Perturbation analysis of simple eigenvalues of polynomial matrices smoothly depending on parameters. Proceedings of ALAMA 2010. pp. 1-7, (2010).

Google Scholar

[7]

I. Gohberg, P. Lancaster, L. Rodman, "Matrix Polynomials", Academic Press, New York, 1982.

Google Scholar

[8]

T. Kato, "Perturbation Theory for Linear Operators", Springer-Verlag, Berlin, 1980.

Google Scholar

[9]

A. P. Seyranian, A.A. Mailybaev, "Multiparameter Stability Theory with Mechanical Applications" World Scientific, Singapore, 2003.

Google Scholar

[10]

G.W. Stewart, J. Sun, "Matrix Perturbation Theory", Academic Press, New York, 1990.

Google Scholar

Perturbation analysis of eigenvalues of polynomial matrices smoothly depending on parameters
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms
2. Mathematics of computing
  1. Mathematical analysis

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Proceedings of the 15th WSEAS international conference on Systems

July 2011

481 pages

ISBN:9781618040237

Editors:
Nikos Mastorakis
Technical University of Sofia, Bulgaria
,
Valeri Mladenov
Technical University of Sofia, Bulgaria
,
Zoran Bojkovic
University of Belgrade, Serbia
,
Fragkiskos Topalis
National Technical University of Athens, Greece
,
Kleanthis Psarris
The University of Texas at San Antonio

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World Scientific and Engineering Academy and Society (WSEAS)

Stevens Point, Wisconsin, United States

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Published: 14 July 2011

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On Eigenvalues of Quadratic Matrix Polynomials and Their Perturbations

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