Inverse spectral problems for semisimple damped vibrating systems

SIAM Journal on Matrix Analysis and Applications

Volumn 29, Issue 1, 2006, Pages 279-301

  Lancaster, Peter ^a  

^a UNIVERSITY OF CALGARY   (Canada)

Author keywords

Inverse problems; Structure preserving transformations; Vibrating systems

Indexed keywords

DAMPING; PROBLEM SOLVING; SET THEORY; SPECTRUM ANALYSIS; SYSTEMS ANALYSIS;

HYPERBOLIC SYSTEMS; STRUCTURE PRESERVING TRANSFORMATIONS; VIBRATING SYSTEMS;

INVERSE PROBLEMS;

EID: 39449116072     PISSN: 08954798     EISSN: 10957162     Source Type: Journal    
DOI: 10.1137/050640187     Document Type: Article

References (16)

1. A. BUNSE-GERSTNER AND W. B. GRAGG, Singular value decompositions of complex symmetric matrices, J. Comput. Appl. Math., 21 (1988), pp. 41-54.
2. R. J. DUFFIN, A minimax theory for overdamped networks, J. Rational Mech. Anal., 4 (1955), pp. 221-233.
3. I. GOHBERG, P. LANCASTER, AND L. RODMAN, Spectral analysis of selfadjoint matrix polynomials, Ann. of Math. (2), 112 (1980), pp. 33-71.
4. I. GOHBERG, P. LANCASTER, AND L. RODMAN, Matrix Polynomials, Academic Press, New York, 1982.
5. G. GOLUB AND C. VAN LOAN, Matrix Computations, 3rd ed., The Johns Hopkins University Press, Baltimore, 1996.
6. C.-H. GUO AND P. LANCASTER, Algorithms for hyperbolic quadratic eigenvalue problems, Math. Comp., 74 (2005), pp. 1777-1791.
7. N. J. HIGHAM, F. TISSEUR, AND P. M. VAN DOOREN, Detecting a definite Hermitian pair and a hyperbolic or elliptic quadratic eigenvalue problem, and associated nearness problems, Linear Algebra Appl., 351/352 (2002), pp. 455-474.
8. R. A. HORN AND C. R. JOHNSON, Matrix Analysis, Cambridge University Press, Cambridge, UK, 1985.
9. P. LANCASTER, Isospectral vibrating systems. Part 1: The spectral method, Linear Algebra Appl., 409 (2005), pp. 51-69.
10. P. LANCASTER AND U. PRELLS, Inverse problems for damped vibrating systems, J. Sound Vibration, 283 (2005), pp. 891-914.
11. P. LANCASTER AND L. RODMAN, Canonical forms for Hermitian matrix pairs under strict equivalence and congruence, SIAM Rev., 47 (2005), pp. 407-443.
12. P. LANCASTER AND M. TISMENETSKY, The Theory of Matrices, Academic Press, Orlando, 1985.
13. P. LANCASTER AND M. TISMENETSKY, Inertia characteristics of self-adjoint matrix polynomials, Linear Algebra Appl., 52/53 (1983), pp. 479-496.
14. P. LANCASTER AND Q. YE, Inverse spectral problems for linear and quadratic matrix pencils, Linear Algebra Appl., 107 (1988), pp. 293-309.
15. U. PRELLS AND P. LANCASTER, Isospectral vibrating systems. II. Structure preserving transformations, in Operator Theory and Indefinite Inner Product Spaces, Oper. Theory Adv. Appl.163, Birkhäuser, Basel, 2006, pp. 275-298.
16. F. TISSEUR AND K. MEERBERGEN, The quadratic eigenvalue problem, SIAM Rev., 43 (2001), pp. 235-286.