The Cayley method and the inverse eigenvalue problem for Toeplitz matrices

BIT Numerical Mathematics

Volumn 42, Issue 2, 2002, Pages 285-299

  Diele, F ^a   Sgura, I ^b  

^a CNR   (Italy)

^b UNIVERSITY OF SALENTO   (Italy)

Author keywords

Cayley methods; Inverse eigenvalue problems; Ordinary differential equations; Toeplitz matrices

Indexed keywords

EID: 0042880822     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1021994807902     Document Type: Article

References (17)

1. D. Boley and G. H. Golub, A survey of matrix inverse eigenvalue problem, Inverse Problems, 3 (1987), pp. 595-622.
2. M. P. Calvo, A. Iserles, and A. Zanna, Numerical solution of isospectral flows, Math. Comp., 66 (1997), pp. 1461-1486.
3. A. Cantoni and P. Butler, Eigenvalue and eigenvectors of symmetric centrosymmetric matrices, Linear Algebra Appl., 13 (1976), pp. 275-288.
4. M. T. Chu, Inverse eigenvalue problem, SIAM Review, 40:1 (1998), pp. 1-39.
5. M. T. Chu, On a differential equation dX/dt = [X, K(X)] where K is a Toeplitz annihilator, Tech. report, North Carolina State University, Rayleigh, NC, 1994.
6. F. Diele, L. Lopez, and R. Peluso, The Cayley transform in the numerical solution of unitary differential systems, Adv. Comput. Math., 8 (1998), pp. 317-334.
7. F. Diele and I. Sgura, Isospectral flows and the inverse eingenvalue problem for Toeplitz matrices, J. Comput. Appl. Math., 110 (1999), pp. 25-43.
8. G. M. L. Gladwell, Inverse Problems in Vibration, Martinus Nijhoff, Dordrecht, Netherlands, 1986.
9. G. H. Golub, Some modified matrix eigenvalue problems, J. SIAM. Review, 15 (1973), pp. 318-334.
10. H. Hochstadt, On construction of a Jacobi matrix from spectral data, Linear Algebra Appl., 8 (1974), pp. 453-446.
11. A. Iserles, H. Z. Munthe-Kaas, S. P. Nørsett, and A. Zanna, Lie-group methods, Acta Numerica, 9 (2000), pp. 215-365.
12. H. J. Landau, The inverse eigenvalue problem for real symmetric Toeplitz matrices, J. Amer. Math. Soc., 7 (1994), pp. 749-767.
13. D. P. Laurie, A numerical approach to the inverse Toeplitz eigenproblem, SIAM J. Sci. Stat. Comput., 9:2 (1988), pp. 401-405.
14. D. P. Laurie, Solving the inverse eigenvalue problem via the eigenvector matrix, J. Comput. Appl. Math., 35 (1991), pp. 277-289.
15. B. N. Parlett, The Symmetric Eigenvalue Problem, Prentice-Hall, Englewood Cliffs, NJ, 1980, reprinted by SIAM, Philadelphia, PA, 1998.
16. R. Peluso, S. Ragni, and I. Sgura, A unifying approach to stability and invariance properties of ODEs, Nonlinear Studies, 5:2 (1998), pp. 173-189.
17. W. F. Trench, Numerical solution of the inverse eigenvalue problem for real symmetric Toeplitz matrices, SIAM J. Sci. Comput., 18:6 (1997), pp. 1722-1736.