Perturbation of partitioned Hermitian definite generalized eigenvalue problems

SIAM Journal on Matrix Analysis and Applications

Volumn 32, Issue 2, 2011, Pages 642-663

  Li, Ren Cang ^a   Nakatsukasa, Yuji ^b   Truhar, Ninoslav ^c   Xu, Shufang ^d  

^a UNIVERSITY OF TEXAS AT ARLINGTON   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c JOSIP JURAJ STROSSMAYER UNIVERSITY OF OSIJEK   (Croatia)

^d PEKING UNIVERSITY   (China)

Author keywords

Generalized eigenvalue problem; Multiple eigenvalue; Quadratic eigenvalue perturbation bound

Indexed keywords

BLOCK DIAGONAL MATRICES; EIGEN-VALUE; EIGENVALUE BOUNDS; EIGENVALUE COMPUTATION; EIGENVALUE PERTURBATION; EIGENVALUES; GENERALIZED EIGENVALUE PROBLEMS; HERMITIAN MATRICES; HERMITIANS; LINEAR ORDER; MATRIX PERTURBATION THEORY; POSITIVE DEFINITE;

LEARNING ALGORITHMS; MATRIX ALGEBRA; PERTURBATION TECHNIQUES; SWITCHING SYSTEMS;

EIGENVALUES AND EIGENFUNCTIONS;

EID: 80051487936     PISSN: 08954798     EISSN: 10957162     Source Type: Journal    
DOI: 10.1137/100808356     Document Type: Article

References (15)

1. R. BHATIA, Matrix Analysis, Grad. Texts in Math. 169, Springer, New York, 1996.
2. Z.-H. CAO, J.-J. XIE, AND R.-C. LI, A sharp version of Kahan's theorem on clustered eigenvalues, Linear Algebra Appl., 245(1996), pp. 147-155. (Pubitemid 126388477)
3. S. C. EISENSTAT AND I. C. F. IPSEN, Relative perturbation techniques for singular value problems, SIAM J. Numer. Anal., 32(1995), pp. 1972-1988.
4. R. A. HORN AND C R. JOHNSON, Matrix Analysis, Cambridge University Press, Cambridge, 1985.
5. W. KAHAN, Inclusion Theorems for Clusters of Eigenvalues of Hermitian Matrices, Technical report, Computer Science Department, University of Toronto, 1967.
6. C.-K. LI AND R.-C. LI, A note on eigenvalues of perturbed hermitian matrices, Linear Algebra Appl., 395(2005), pp. 183-190.
7. C.-K. LI AND R. MATHIAS, The Lidskii-Mirsky-Wielandt theorem-additive and multiplicative versions, Numer. Math., 81, pp. 377-413.
8. R.-C. LI, Relative perturbation theory I. Eigenvalue and singular value variations, SIAM J. Matrix Anal. Appl., 19(1998), pp. 956-982.
9. R.-C. LI, Matrix perturbation theory, in Handbook of Linear Algebra, L. Hogben, R. Brualdi, A. Greenbaum, and R. Mathias, eds., CRC Press, Boca Raton, FL, 2006.
10. R. MATHIAS, Quadratic residual bounds for the Hermitian eigenvalue problem, SIAM J. Matrix Anal. Appl., 19(1998), pp. 541-550.
11. Y. NAKATSUKASA, Perturbation behavior of a multiple eigenvalue in generalized Hermitian eigenvalue problems, BIT, 50(2010), pp. 109-121.
12. A. M. OSTROWSKI, A quantitative formulation of Sylvester's law of inertia, Proc. Natl. Acad. Sci. U. S. A., 45(1959), pp. 740-744.
13. B. N. PARLETT, The Symmetric Eigenvalue Problem, SIAM, Philadelphia, 1998.
14. G. W. STEWART AND J.-G. SUN, Matrix Perturbation Theory, Academic Press, Boston, 1990.
15. J.-G. SUN, Eigenvalues of Rayleigh quotient matrices, Numer. Math., 59(1991), pp. 603-614.