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Displacement ranks of a matrix. (English) Zbl 0417.65015


MSC:

65F05 Direct numerical methods for linear systems and matrix inversion
15A09 Theory of matrix inversion and generalized inverses
15B57 Hermitian, skew-Hermitian, and related matrices
47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators
68Q25 Analysis of algorithms and problem complexity
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References:

[1] Thomas Kailath, Some new algorithms for recursive estimation in constant linear systems, IEEE Trans. Information Theory IT-19 (1973), 750 – 760. · Zbl 0342.93053
[2] M. Morf, G. S. Sidhu and T. Kailath, Some new algorithms for recursive estimation in constant, linear, discrete-time systems, IEEE Trans. Automatic Control AC-19 (1974), 315-323. · Zbl 0279.93043
[3] M. Morf, Fast algorithms for multivariate systems, Ph.D. Dissertation, Stanford University, Stanford, Calif., 1974.
[4] Thomas Kailath, Lennart Ljung, and Martin Morf, Generalized Kreĭn-Levinson equations for efficient calculation of Fredholm resolvents of nondisplacement kernels, Topics in functional analysis (essays dedicated to M. G. Kreĭn on the occasion of his 70th birthday), Adv. in Math. Suppl. Stud., vol. 3, Academic Press, New York-London, 1978, pp. 169 – 184. · Zbl 0441.45007
[5] I. C. Gohberg and I. A. Fel\(^{\prime}\)dman, Convolution equations and projection methods for their solution, American Mathematical Society, Providence, R.I., 1974. Translated from the Russian by F. M. Goldware; Translations of Mathematical Monographs, Vol. 41.
[6] T. Kailath, A. Vieira, and M. Morf, Inverses of Toeplitz operators, innovations, and orthogonal polynomials, SIAM Rev. 20 (1978), no. 1, 106 – 119. · Zbl 0382.47013 · doi:10.1137/1020006
[7] Alfred V. Aho, John E. Hopcroft, and Jeffrey D. Ullman, The design and analysis of computer algorithms, Addison-Wesley Publishing Co., Reading, Mass.-London-Amsterdam, 1975. Second printing; Addison-Wesley Series in Computer Science and Information Processing. · Zbl 0326.68005
[8] M. Morf, Doubling algorithms for Toeplitz and related equations, IEEE Trans. Information Theory (submitted).
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