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Moment problems and low rank Toeplitz approximations. (English) Zbl 0507.65011

65F30 Other matrix algorithms (MSC2010)
44A60 Moment problems
15A63 Quadratic and bilinear forms, inner products
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[1] R. Bartels, G.H. Golub, and C. van Loan, Applied Matrix Computations, manuscript, to be published by Johns Hopkins University Press.
[2] G. Cybenko,The numerical stability of the Levinson-Durbin algorithm for Toeplitz systems of equations, SIAM J. Sci. Stat. Comput., 1 (1980), pp. 303–319. · Zbl 0474.65026
[3] G. Cybenko, Affine minimax problems and semi-infinite programming, submitted to Mathematical Programming. · Zbl 0507.65011
[4] B.W. Dickinson,Two-dimensional Markov spectrum estimates need not exist, IEEE Trans. Information Sci., 26 (1980), pp. 120–121.
[5] J. Durbin,The fitting of time-series models, Rev. Int. Inst. Statist., 28 (1960) pp. 233–243. · Zbl 0101.35604
[6] G.H. Golub and V. Pereyra,The differentiation of pseduo-inverses and nonlinear least squares problems whose variables separate, SIAM J. Num. Anal., 10 (1973), pp. 413–432. · Zbl 0258.65045
[7] W.B. Gragg, Positive definite Toeplitz matrices, the Hessenberg process for isometric operators, and Gaussian quadrature on the unit circle, to appear, in Russian, in Sbornik Moscow State University. · Zbl 0554.65027
[8] U. Grenender and G. Szegö,Toeplitz Forms and their Applications, University of California Press, Berkeley, 1958.
[9] S.Y. Kung, A Toeplitz approximation method and some applications, International Symposium on Mathematical Theory of Networks and Systems, Santa Monica, California, August 1981.
[10] N. Levinson,The Weiner RMS (root mean square) error criterion in filter design and prediction, J. Math. Phys., 45 (1947), pp. 261–278.
[11] J. Makhoul,Linear prediction: a tutorial review, Proc. IEEE, 63 (1975), pp. 561–580.
[12] V.F. Pisarenko,The retrieval of harmonics from a covariance function, Geophysics J.R. Astr. Soc., 33 (1973) pp. 347–366. · Zbl 0287.62048
[13] L.R. Rabiner and R. Schafer,Digital Processing of Speech Signals, Prentice Hall, Englewood Cliffs, 1978. · Zbl 1162.94003
[14] W.W. Rogosinski,Moments of non-negative mass, Proc. Roy. Soc. (London), Series A, 245 (1958) pp. 1–27. · Zbl 0082.32404
[15] W. Rudin,Fourier Analysis on Groups, Wiley Interscience, New York, 1960. · Zbl 0099.32201
[16] W. Rudin,The extension problem for positive-definite functions, Ill J. Math., 7 (1963), pp. 532–539. · Zbl 0114.31003
[17] G.W. Stewart,A modification of Davidon’s minimization method to accept difference approximations of derivatives, J. Assoc. Comp. Mach., 14 (1967) pp. 72–83. · Zbl 0239.65056
[18] V.M. Tschakaloff,Formules de cubature méchanique à coefficients non négatifs, Bull. Sci. Math., 81 (1957), pp. 123–134.
[19] S.W. Lang and J.H. McClellan,Spectral estimation for sensor arrays, Proceedings of First ASSP Workshop in Spectral Estimation, Hamilton, Ontario, August 17–18, 1981, pp. 3.2.1–3.2.7.
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