On the elementwise convergence of continuous functions of hermitian banded Toeplitz matrices

IEEE Transactions on Information Theory

Volumn 53, Issue 3, 2007, Pages 1168-1176

  Crespo, Pedro M ^a   Gutiérrez Gutiérrez, Jesús ^a  

^a CEIT   (Spain)

Author keywords

Circulant matrices; Covariance matrices; Elementwise convergence; Functions of matrices; Minimum mean square error (MMSE); Stationary stochastic time series; Szeg 's theorem; Toeplitz matrices

Indexed keywords

ASYMPTOTIC ANALYSIS; CONVERGENCE OF NUMERICAL METHODS; COVARIANCE MATRIX; MEAN SQUARE ERROR; STOCHASTIC MODELS; TIME SERIES ANALYSIS;

CIRCULANT MATRIX; CONTINUOUS FUNCTION; TOEPLITZ MATRIX;

INFORMATION THEORY;

EID: 33947640538     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2006.890697     Document Type: Article

References (21)

1. U. Grenander and G. Szegö, Toeplitz Forms and Their Applications. Berkeley, CA: University of California Press, 1958.
2. R. M. Gray, "Toeplitz and circulant matrices: A review," Found. Trends Commun. Inf. Theory, vol. 2, no. 3, pp. 155-239, 2006, [Original version: Tech. Rep. 6502-1, Stanford Electronic Lab., Stanford, CA, June 1971].
3. R. M. Gray, "On the asymptotic eigenvalue distribution of Toeplitz matrices," IEEE Trans. Inf. Theory, vol. 18, pp. 725-730, Nov. 1972.
4. J. Pearl, "On coding and filtering stationary signals by discrete Fourier transforms," IEEE Trans. Inf. Theory, vol. 19, pp. 229-232, Mar. 1973.
5. J. Pearl, "Basis-restricted transformations and performance measures for spectral representation," IEEE Trans. Inf. Theory, vol. 17, pp. 751-752, Nov. 1971.
6. P. J. Sherman, "Circulant approximations of the inverses of Toeplitz matrices and related quantities with applications to stationary random processes," IEEE Trans. Acoust., Speech, Signal Processing, vol. 33, pp. 1630-1632, Dec. 1985.
7. P. M. Crespo and J. Gutiérrez-Gutiérrez, "On the application of asymptotically equivalent sequences of matrices to the derivation of the continuous time Gaussian channel capacity," AEÜ-Int. J. Electron. Commun., vol. 60, no. 8, pp. 573-581, 2006.
8. S. Haykin, Adaptive Filter Theory. Englewood Clifff, NJ: Prentice-Hall, 1986.
9. B. S. Tsybakov, "Capacity of a discrete-time Gaussian channel with a filter," Probl. Inform. Transm., vol. 6, pp. 253-256, Jul.-Sep. 1970.
10. W. Hirt and J. L. Massey, "Capacity of the discrete-time Gaussian channel with intersymbol interference," IEEE Trans. Inf. Theory, vol. 34, pp. 380-388, May 1988.
11. F. R. Gantmacher, The Theory of Matrices. New York: Chelsea, 1977, vol. 1.
12. R. A. Horn and C. R. Johnson, Topics in Matrix Analysis. New York: Cambridge University Press, 1994.
13. R. A. Horn, Matrix Analysis. New York: Cambridge University Press, 1990.
14. W. F. Trench, "Absolute equal distribution of the spectra of Hermitian matrices," Linear Algebra Appl., vol. 366, pp. 417-431, 2003.
15. A. Böttcher; and B. Silbermann, Introduction to Large Truncated Toeplitz Matrices. New York: Springer, 1999.
16. G. H. Golub and C. F. Van Loan, Matrix Computation. Baltimore, MD: The John Hopkins University Press, 1987.
17. W. F. Trench, "On the eigenvalue problem for Toeplitz band matrices," Linear Algebra Appl., vol. 64, pp. 199-214, 1985.
18. S. U. H. Qureshi, "Adaptive equalization," Proc. IEEE, vol. 73, no. 9, pp. 1349-1387, 1985.
19. A. Böttcher, J. Gutiérrez-Gutiérrez, and P. M. Crespo, "Mass concentration in quasicommutators of Toeplitz matrices," J. Comput. Appl. Math., to be published.
20. J. Salz, "On mean-square decision feedback equalization and timing phase," IEEE Trans. Commun., vol. 25, pp. 1471-1476, Dec. 1977.
21. E. Zeidler, Applied Functional Analysis: Main Principles and Their Applications, ser. Applied Mathematical Sciences. New York: Springer-Verlag, 1995, vol. 109.