Detecting a definite Hermitian pair and a hyperbolic or elliptic quadratic eigenvalue problem, and associated nearness problems

Linear Algebra and Its Applications

Volumn 351-352, Issue , 2002, Pages 455-474

  Higham, Nicholas J ^a   Tisseur, Françoise ^a   Van Dooren, Paul M ^b  

^a UNIVERSITY OF MANCHESTER   (United Kingdom)

^b UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

Author keywords

Bisection algorithm; Crawford number; Definite pair; Elliptic system; Gyroscopic system; Hermitian generalized eigenvalue problem; Hermitian quadratic eigenvalue problem; Hyperbolic system; Level set algorithm; Nearness problems; Overdamped system

Indexed keywords

ALGORITHMS; COMPUTATION THEORY; DEGREES OF FREEDOM (MECHANICS); LEARNING ALGORITHMS; SWITCHING SYSTEMS;

BISECTION ALGORITHMS; CRAWFORD NUMBER; DEFINITE PAIR; ELLIPTIC SYSTEM; GENERALIZED EIGENVALUE PROBLEMS; GYROSCOPIC SYSTEM; HYPERBOLIC SYSTEM; LEVEL SET ALGORITHM; NEARNESS PROBLEMS; OVERDAMPED SYSTEMS; QUADRATIC EIGENVALUE PROBLEMS;

EIGENVALUES AND EIGENFUNCTIONS;

EID: 31244435530     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(02)00281-1     Document Type: Article

References (25)

1. L. Barkwell, and P. Lancaster Overdamped and gyroscopic vibrating systems Trans. AME: J. Appl. Mech. 59 1992 176 181
2. R. Byers A bisection method for measuring the distance of a stable matrix to the unstable matrices SIAM J. Sci. Statist. Comput. 9 5 1988 875 881
3. S.H. Cheng, and N.J. Higham The nearest definite pair for the Hermitian generalized eigenvalue problem Linear Algebra Appl. 302-303 1999 63 76
4. C.R. Crawford ALGORITHM 646 PDFIND: A routine to find a positive definite linear combination of two real symmetric matrices ACM Trans. Math. Software 12 1986 278 282
5. C.R. Crawford, and Y.S. Moon Finding a positive definite linear combination of two Hermitian matrices Linear Algebra Appl. 51 1983 37 48
6. J. Doyle Analysis of feedback systems with structured uncertainties IEE Proc. D 129 6 1982 242 250
7. R.J. Duffin A minimax theory for overdamped networks J. Rat. Mech. Anal. 4 1955 221 233
8. R.J. Duffin The Rayleigh-Ritz method for dissipative or gyroscopic systems Quart. Appl. Math. 18 3 1960 215 221
9. M.K.H. Fan, An algorithm to compute the structured singular value, Technical Report TR-86-8, System Research Center, University of Maryland, 1986
10. P. Freitas, M. Grinfield, and P. Knight Stability of finite-dimensional systems with indefinite damping Adv. Math. Sci. Appl. 17 1 1997 435 446
11. ∞ -norms and related questions in: Proceedings of the International Symposium MTNS-98, Padova, Italy 1998 429 432
12. N.J. Higham, The Test Matrix Toolbox for MATLAB (version 3.0), Numerical Analysis Report No. 276, Manchester Centre for Computational Mathematics, Manchester, England, 1995
13. T. Kato Perturbation Theory for Linear Operators second ed. 1976 Springer Berlin
14. P. Lancaster Lambda-Matrices and Vibrating Systems 1966 Pergamon Press Oxford
15. P. Lancaster Quadratic eigenvalue problems Linear Algebra Appl. 150 1991 499 506
16. A.S. Markus Introduction to the Spectral Theory of Polynomial Operator Pencils 1988 AMS Providence, RI
17. B.N. Parlett Symmetric matrix pencils J. Comp. Appl. Math. 38 1991 373 385
18. J. Sreedhar, P.V. Dooren, and A.L. Tits A fast algorithm to compute the real structured stability radius R. Jeltsch, M. Mansour, Stability Theory: Proceedings of Hurwitz Centenary Conference, Ticino, Switzerland 1995 1996 Birkhäuser Basel 219 230
19. G.W. Stewart Perturbation bounds for the definite generalized eigenvalue problem Linear Algebra Appl. 23 1979 69 85
20. G.W. Stewart, and J. Sun Matrix Perturbation Theory 1990 Academic Press London
21. F. Tisseur Backward error and condition of polynomial eigenvalue problems Linear Algebra Appl. 309 2000 339 361
22. F. Tisseur, and K. Meerbergen The quadratic eigenvalue problem SIAM Rev. 43 2 2001 235 286
23. M.J. Todd Semidefinite optimization Acta Numerica 10 2001 515 560
24. K. Veselić A Jacobi eigenreduction algorithm for definite matrix pairs Numer. Math. 64 1993 241 269
25. S. Wei, and I. Kao Vibration analysis of wire and frequency response in the modern wiresaw manufacturing process J. Sound Vibration 231 5 2000 1383 1395