On Polynomial Maximum Entropy Method for Classical Moment Problem

2015 ◽  
Vol 8 (1) ◽  
pp. 117-127
Author(s):  
Jiu Ding ◽  
Noah H. Rhee ◽  
Chenhua Zhang
Keyword(s):  
Maximum Entropy ◽  
Moment Problem ◽  
Maximum Entropy Method ◽  
Entropy Method ◽  
Moment Problems ◽  
Monomial Basis ◽  
Ill Conditioning ◽  
Legendre Moment ◽  
Hausdorff Moment Problem ◽  
Classical Moment Problem

AbstractThe maximum entropy method for the Hausdorff moment problem suffers from ill conditioning as it uses monomial basis {1,x,x2,...,xn}. The maximum entropy method for the Chebyshev moment probelm was studied to overcome this drawback in. In this paper we review and modify the maximum entropy method for the Hausdorff and Chebyshev moment problems studied in and present the maximum entropy method for the Legendre moment problem. We also give the algorithms of converting the Hausdorff moments into the Chebyshev and Lengendre moments, respectively, and utilizing the corresponding maximum entropy method.

A Maximum Entropy Method Based on Orthogonal Polynomials for Frobenius-Perron Operators

2011 ◽  
Vol 3 (2) ◽  
pp. 204-218 ◽  
Author(s):  
Jiu Ding ◽  
Noah H. Rhee
Keyword(s):  
Orthogonal Polynomials ◽  
Maximum Entropy ◽  
Moment Problem ◽  
Chebyshev Polynomials ◽  
Numerical Experiments ◽  
Maximum Entropy Method ◽  
Chaotic Map ◽  
Entropy Method ◽  
The Stability ◽  
Stability Consideration

AbstractLet S: [0, 1]→[0, 1] be a chaotic map and let f* be a stationary density of the Frobenius-Perron operator PS: L1→L1 associated with S. We develop a numerical algorithm for approximating f*, using the maximum entropy approach to an under-determined moment problem and the Chebyshev polynomials for the stability consideration. Numerical experiments show considerable improvements to both the original maximum entropy method and the discrete maximum entropy method.

Enhanced Information Recovery in 2D On-and Off-Resonance Nutation NQR using the Maximum Entropy Method

1996 ◽  
Vol 51 (5-6) ◽  
pp. 337-347 ◽  
Author(s):  
Mariusz Maćkowiak ◽  
Piotr Kątowski
Keyword(s):  
Maximum Entropy ◽  
Maximum Entropy Method ◽  
Theoretical Description ◽  
Entropy Method ◽  
Zero Field ◽  
Resonance Effects ◽  
Information Recovery ◽  
Truncation Errors ◽  
Enhanced Resolution ◽  
2D Data

Abstract Two-dimensional zero-field nutation NQR spectroscopy has been used to determine the full quadrupolar tensor of spin - 3/2 nuclei in serveral molecular crystals containing the 3 5 Cl and 7 5 As nuclei. The problems of reconstructing 2D-nutation NQR spectra using conventional methods and the advantages of using implementation of the maximum entropy method (MEM) are analyzed. It is shown that the replacement of conventional Fourier transform by an alternative data processing by MEM in 2D NQR spectroscopy leads to sensitivity improvement, reduction of instrumental artefacts and truncation errors, shortened data acquisition times and suppression of noise, while at the same time increasing the resolution. The effects of off-resonance irradiation in nutation experiments are demonstrated both experimentally and theoretically. It is shown that off-resonance nutation spectroscopy is a useful extension of the conventional on-resonance experiments, thus facilitating the determination of asymmetry parameters in multiple spectrum. The theoretical description of the off-resonance effects in 2D nutation NQR spectroscopy is given, and general exact formulas for the asymmetry parameter are obtained. In off-resonance conditions, the resolution of the nutation NQR spectrum decreases with the spectrometer offset. However, an enhanced resolution can be achieved by using the maximum entropy method in 2D-data reconstruction.

Estimating the distribution of primary reflection coefficients

Geophysics ◽  
2003 ◽  
Vol 68 (4) ◽  
pp. 1417-1422 ◽  
Author(s):  
Danilo R. Velis
Keyword(s):  
Maximum Entropy ◽  
Maximum Entropy Method ◽  
Entropy Method ◽  
Reflection Coefficients ◽  
Log Data ◽  
Neuquen Basin ◽  
Neuquén Basin ◽  
Skewness And Kurtosis

The distribution of primary reflection coefficients can be estimated by means of the maximum entropy method, giving rise to smooth nonparametric functions which are consistent with the data. Instead of using classical moments (e.g. skewness and kurtosis) to constraint the maximization, nonconventional sample statistics help to improve the quality of the estimates. Results using real log data from various wells located in the Neuquen Basin (Argentina) show the effectiveness of the method to estimate both robust and consistent distributions that may be used to simulate realistic sequences.

Maximum entropy method in phase-encoding NMR imaging

1987 ◽  
Vol 4 (1) ◽  
pp. 78-82 ◽  
Author(s):  
B. C. De Simone ◽  
F. De Luca ◽  
B. Maraviglia
Keyword(s):  
Maximum Entropy ◽  
Maximum Entropy Method ◽  
Entropy Method ◽  
Nmr Imaging ◽  
Phase Encoding
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