On the Lidskii-Vishik-Lyusternik perturbation theory for eigenvalues of matrices with arbitrary Jordan structure

SIAM Journal on Matrix Analysis and Applications

Volumn 18, Issue 4, 1997, Pages 793-817

  Moro, Julio ^a   Burke, James V ^b   Overton, Michael L ^c  

^a UNIVERSIDAD CARLOS III DE MADRID   (Spain)

^b UNIVERSITY OF WASHINGTON   (United States)

^c POLYTECHNIC UNIVERSITY   (United States)

Author keywords

Newton diagram; Newton envelope; Perturbation of eigenvalues; Perturbation theory for linear operators; Spectral condition number; Stability theory

Indexed keywords

EID: 0031497208     PISSN: 08954798     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895479895294666     Document Type: Article

References (16)

1. H. BAUMGÄRTEL, Analytic Perturbation Theory for Matrices and Operators, Birkhäuser-Verlag, Basel, Switzerland, 1985.
2. J. V. BURKE AND M. L. OVERTON, Stable perturbations of nonsymmetric matrices, Linear Algebra Appl., 171 (1992), pp. 249-273.
3. J. V. BURKE AND M. L. OVERTON, Differential properties of the spectral abscissa and the spectral radius for analytic matrix-valued mappings, Nonlinear Anal., 23 (1994), pp. 467-488.
4. F. CHATELIN, Eigenvalues of Matrices, John Wiley, New York, 1993.
5. G. GOLUB AND C. F. VAN LOAN, Matrix Computations, 1st ed., The Johns Hopkins University Press, Baltimore, MD, 1983.
6. R. HORN AND C. R. JOHNSON, Matrix Analysis, Cambridge University Press, Cambridge, UK, 1990.
7. T. KATO, Perturbation Theory for Linear Operators, Springer-Verlag, Berlin, 1980.
8. H. LANGER AND B. NAJMAN, Remarks on the perturbation of analytic matrix functions III, Integral Equations Operator Theory, 15 (1992), pp. 796-806.
9. H. LANGER AND B. NAJMAN, Leading coefficients of the eigenvalues of perturbed analytic matrix functions, Integral Equations Operator Theory, 16 (1993), pp. 600-604.
10. V. B. LIDSKII, Perturbation theory of non-conjugate operators, U.S.S.R. Comput. Math. and Math. Phys., 1 (1965), pp. 73-85 (Zh. vychisl. Mat. mat. Fiz., 6 (1965), pp. 52-60).
11. V. B. LIDSKII, Perturbation theory of non-conjugate operators, U.S.S.R. Comput. Math. and Math. Phys., 1 (1965), pp. 73-85 (Zh. vychisl. Mat. mat. Fiz., 6 (1965), pp. 52-60).
12. J. H. MADDOCKS AND M. L. OVERTON, Stability theory for dissipatively perturbed Hamiltonian systems, Comm. Pure Appl. Math., 48 (1995), pp. 583-610.
13. M. M. VAINBERG AND V. A. TRENOGIN, Theory of Branching of Solutions of Non-linear Equations, P. Noordhoff, Leyden, 1974.
14. M. I. VISHIK AND L. A. LYUSTERNIK, The solution of some perturbation problems for matrices and selfadjoint or non-selfadjoint differential equations I, Russian Math. Surveys, 15 (1960), pp. 1-74 (Uspekhi Mat. Nauk, 15 (1960), pp. 3-80).
15. M. I. VISHIK AND L. A. LYUSTERNIK, The solution of some perturbation problems for matrices and selfadjoint or non-selfadjoint differential equations I, Russian Math. Surveys, 15 (1960), pp. 1-74 (Uspekhi Mat. Nauk, 15 (1960), pp. 3-80).
16. J. H. WILKINSON, The Algebraic Eigenvalue Problem, Clarendon, Oxford, UK, 1965.