Available in electronic format
Available in print format
Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)
     

Maximum entropy and the moment problem

Author(s): H. J. Landau
Journal: Bull. Amer. Math. Soc. 16 (1987), 47-77.
MSC (1985): Primary 42A70; Secondary 42A05, 62M15, 94A17, 60G25
MathSciNet review: 866018
Retrieve article in: PDF

References | Similar articles | Additional information

References:

1.
N. I. Akhiezer, The classical moment problem, Hafner, New York, 1965.
2.
L. Breiman, Probability and stochastic processes, Houghton-Mifflin, Boston, 1969.
3.
A. M. Bruckstein and T. Kailath, Inverse scattering for discrete transmission-line models, SIAM Review 7 (1986), 1332-1349. MR 902563
4.
A. M. Bruckstein, B. C. Levy, and T. Kailath, Differential methods in inverse scattering, SIAM J. Appl. Math. 45 (1985), 312-335. MR 781110
5.
A. Bultheel, Error analysis of incoming and outgoing schemes for the trigonometric moment problem, Padé Approximation and Applications, Lecture Notes in Math., vol. 888, Springer-Verlag, Berlin and New York, 1981, pp. 100-109. MR 649088
6.
J. P. Burg, Maximum entropy spectral analysis, Proc. 37th Meet. Soc. Exploration Geophysicists, 1967; reprinted in Modern Spectrum Analysis (D. G. Childers, ed.), IEEE Press, New York, 1978, pp. 34-39.
7.
J. P. Burg, A new analysis technique for time series data, NATO Adv. Study Inst, on Signal Processing, Enschede, Netherlands, 1968; reprinted in Modern Spectrum Analysis (D. G. Childers, ed.), IEEE Press, New York, 1978, 42-48.
8.
J. P. Burg, The relationship between maximum entropy spectra and maximum likelihood spectra, Geophysics, 1972; reprinted in Modern Spectrum Analysis (D. G. Childers, ed.), IEEE Press, New, York, 1978, pp. 132-133.
9.
J. P. Burg, Maximum entropy spectral analysis, Ph.D. dissertation, Stanford University, Stanford, California, 1975.
10.
D. G. Childers, ed., Modern spectrum analysis, IEEE Press, New York, 1978.
11.
B. S. Choi and T. M. Cover, An information-theoretic proof of Burg's maximum entropy spectrum, Proc. IEEE 72 (1984), 1094-1095.
12.
I. Csiszàr and G. Tusnàdy, Information geometry and alternating minimization procedures, Statist. Decisions (1984), Suppl. 1, 205-237. MR 785210
13.
A. P. Dempster, N. M. Laird, and D. B. Rubin, Maximum likelihood from incomplete data via the EM algorithm, J. Royal Stat. Soc. Ser. B 39 (1977), 1-38. MR 501537
14.
H. Dym and A. Iacob, Applications of factorization and Toeplitz operators to inverse problems, Toeplitz Centennial Memorial Conference (I. Gohberg, ed.), Birkhäuser, Basel-Boston-Stuttgart, 1982, pp. 233-260. MR 669911
15.
I. C. Gohberg and I. A. Fel'dman, Convolution equations and projection methods for their solution, Transl. Math. Monographs, vol. 41, Amer. Math. Soc. Providence, RI, 1974. MR 355675
16.
B. Gopinath and M. M. Sondhi, Inversion of the telegraph equation and the synthesis of non-uniform lines, Proc. IEEE 59 (1971), 383-392. MR 339916
17.
U. Grenander and G. Szegö, Toeplitz forms and their applications, Univ. of Calif. Press, Berkeley, 1957. MR 94840
18.
S. Haykin, ed., Nonlinear methods of spectral analysis, Springer-Verlag, New York, 1979. MR 601216
19.
K. Hoffman, Banach spaces of analytic functions, Prentice-Hall, New York, 1962. MR 133008
20.
E. T. Jaynes, On the rationale of maximum entropy methods, Proc. IEEE 70 (1982), 939-952.
21.
T. Kailath, A theorem of I. Schur and its impact on modern signal processing, I. Schur Methods in Operator Theory and Signal Processing (I. Gohberg, ed.), Operator Theory: Advances and Applications, vol. 18, Birkhàuser, Basel-Boston-Stuttgart, 1986, pp. 9-30. MR 902601
22.
T. Kailath, A. Bruckstein, D. Morgan, Fast matrix factorizations via discrete transmission lines, Linear Algebra Appl. 75 (1986), 1-25. MR 825396
23.
T. Kailath and H. Lev-Ari, On mappings between covariance matrices and physical systems, Contemporary Mathematics (B. Datta, ed.), Amer. Math. Soc. vol. 47, Providence, R.I., 1985, pp. 241-252. MR 828304
24.
T. Kailath, A. Vieira, and M. Morf, Inverses of Toeplitz operators, innovations, and orthogonal polynomials, SIAM Review 20 (1978), 106-119. MR 512865
25.
S. J. Karlin and W. J. Studden, Tchebycheff systems: With applications in analysis and statistics, Interscience, New York, 1966.
26.
M. G. Krein, The ideas of P. L. Čebyšev and A. A. Markov in the theory of limiting values of integrals and their further development, Uspehi Mat. Nauk (NS) 6 (1951), 3-120; Amer. Math. Soc. Transl. Ser. 2, 12 (1959), 1-122. MR 44591
27.
M. G. Krein, Solution of the inverse Sturm-Liouville problem, Dokl. Akad. Nauk SSSR 76 (1951), 21-24. (Russian) MR 39895
28.
M. G. Krein, On integral equations which generate second-order differential equations, Dokl. Akad. Nauk SSSR 97 (1954), 21-24. (Russian) MR 65016
29.
M. G. Krein, Continuous analogues of propositions on polynomials orthogonal on the unit circle, Dokl. Akad. Nauk SSSR 105 (1955), 637-640. (Russian) MR 80735
30.
R. T. Lacoss, Autoregressive and maximum likelihood spectral analysis methods, Aspects of Signal Processing, Part 2, NATO Adv. Study Inst., La Spezia, Italy, 1976 (G. Tacconi, ed.), D. Reidel, Boston, pp. 591-615.
31.
H. J. Landau, The inverse problem for the vocal tract and the moment problem, SIAM J. Math. Anal. 14 (1983), 1019-1035. MR 711183
32.
H. Lev-Ari and T. Kailath, Lattice-filter parametrization and modeling of nonstationary processes, IEEE Trans. Inf. Theory IT-30 (1984), 2-16. MR 730996
33.
T. L. Marzetta and S. W. Lang, Power spectral density bounds, IEEE Trans. Inf. Theory IT-30 (1984), 117-122.
34.
A. Papoulis, Maximum entropy and spectral estimation: a review, IEEE Trans. Acoustics, Speech, and Signal Proc. ASSP-29 (1981), 1176-1186. MR 642904
35.
E. A. Robinson, Spectral approach to geophysical inversion by Lorentz, Fourier, and Radon transforms, Proc. IEEE 70 (1982), 1039-1054.
36.
J. E. Shore and R. W. Johnson, Axiomatic derivation of the principle of maximum entropy and the principle of minimum cross-entropy, IEEE Trans. Inf. Theory IT-26 (1980), 26-37; Comments and corrections, IEEE Trans. Inf. Theory IT-29 (1983), 942-943. MR 733203
37.
J. E. Shore and R. W. Johnson, Properties of cross-entropy minimization, IEEE Trans. Inf. Theory IT-27 (1981) 472-482. MR 635526
38.
J. M. Van Campenhout and T. M. Cover, Maximum entropy and conditional probability, IEEE Trans. Inf. Theory IT-27 (1981), 483-489. MR 635527
39.
Y. Vardi, L. A. Shepp, and L. Kaufman, A statistical model for positron emission tomography, J. Amer. Statist. Assoc. 80 (1985), 8-37. MR 786595

Similar Articles:

Retrieve articles in Bulletin of the American Mathematical Society with MSC (1985): 42A70, 42A05, 62M15, 94A17, 60G25

Retrieve articles in all Journals with MSC (1985): 42A70, 42A05, 62M15, 94A17, 60G25


Additional Information:

DOI: 10.1090/S0273-0979-1987-15464-4
PII: S 0273-0979(1987)15464-4


  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement
Search the AMSPowered by Google