Locally Toeplitz sequences: Spectral properties and applications

Linear Algebra and Its Applications

Volumn 278, Issue 1-3, 1998, Pages 91-120

  Tilli, P ^a  

^a SCUOLA NORMALE SUPERIORE   (Italy)

Author keywords

Eigenvalues; Locally Toeplitz; Singular values; Spectral distribution

Indexed keywords

EID: 11544297717     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(97)10079-9     Document Type: Article

References (17)

1. U. Grenander, G. Szego, Toeplitz Forms and their Applications, 2nd ed., 1984, Chelsea, New York.
2. E.E. Tyrtyshnikov, A unifying approach to some old and new theorems on distribution and clustering, Linear Algebra Appl. 232 (1996) 1-43.
3. E.E. Tyrtyshnikov, N. Zamarashkin, Spectra of multilevel Toeplitz matrices: advanced Theory via simple matrix relationships, Linear Algebra Appl. 270 (1998) 15-27.
4. P. Tilli, Singular values and eigenvalues of non-Hermitian block Toeplitz matrices, Linear Algebra Appl. 272 (1998) 59-80.
5. H. Widom, Asymptotic behaviour of block Toeplitz matrices and determinants, Advances in Math. 13 (1974) 284-322.
6. H. Widom, Szego limit theorem: the higher dimensional matrix case, J. Func. Anal. 39 (1980) 182-198.
7. H. Widom, On the limit of block Toeplitz determinants, Proc. Amer. Math. Soc. 50 (1975) 167-173.
8. F. Avram, On bilinear forms on Gaussian random variables and Toeplitz matrices, Probab. Theory Related Fields 79 (1988) 37-45.
9. S.V. Parter, On the distribution of the singular values of Toeplitz matrices, Linear Algebra Appl. 80 (1986) 115-130.
10. G. Fiorentino, S. Serra, Tau preconditioners for (high order) elliptic problems, in: Vassilevski (Ed.), Proceedings of the second IMACS conference on Iterative Methods in Linear Algebra, Blagoevgrad, Bulgaria, 1995, pp. 241-252.
11. L. Collatz, The Numerical Treatment of Differential Equations, 3rd ed., Springer, Berlin, 1960.
12. E.E. Tyrtyshnikov, Influence of matrix operations on the distribution of eigenvalues and singular values of Toeplitz matrices, Linear Algebra Appl. 207 (1994) 225-249.
13. S. Serra, The rate of convergence of Toeplitz based PCG methods for second order nonlinear boundary value problems, Num. Mat., to appear.
14. T. Kailath, A.S. Sayed, Displacement structure: theory and applications, SIAM Rev. 37 (3) (1995) 297-386.
15. W. Rudin, Real and Complex Analysis, McGraw-Hill, New York, 1974.
16. P. Halmos, Measure Theory, Springer, New York, 1974.
17. R.A. Horn, C.R. Johnson, Matrix Analysis, Cambridge University Press, Cambridge, 1985.