On the Convergence of an Efficient Algorithm for Kullback-Leibler Approximation of Spectral Densities

This paper deals with a method for the approximation of a spectral density function among the solutions of a generalized moment problem à la Byrnes/Georgiou/Lindquist. The approximation is pursued with respect to the Kullback-Leibler pseudo-distance, which gives rise to a convex optimization proble...

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Veröffentlicht in:IEEE transactions on automatic control Jg. 56; H. 3; S. 506 - 515
Hauptverfasser: Ferrante, Augusto, Ramponi, Federico, Ticozzi, Francesco
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York, NY IEEE 01.03.2011
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
Algorithm design and analysis
Algorithms
Applied sciences
Approximation
Approximation algorithms
Calculus of variations and optimal control
Collaboration
Convergence
Convergence of numerical methods
Density
Density functional theory
Distribution theory
Exact sciences and technology
Filter bank
Frequency estimation
History
Information theory
Information, signal and communications theory
Interpolation
Kullback-Leibler pseudo-distance
Manifolds
Mathematical analysis
Mathematical models
Mathematics
Optimization
Probability and statistics
Robust control
Sciences and techniques of general use
Spectra
spectral estimation
Statistics
Telecommunications and information theory
Spectral function
spectral estimation
Generalized solution
Entropy
Kullback―Leibler pseudo-distance
Convex programming
Global solution
Spectral analysis
Information measure
Manifold
Efficiency
Approximation method
Variational calculus
Moment problem
Density function
Spectral density
Dual space
Numerical convergence
ISSN:0018-9286, 1558-2523
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Zusammenfassung:This paper deals with a method for the approximation of a spectral density function among the solutions of a generalized moment problem à la Byrnes/Georgiou/Lindquist. The approximation is pursued with respect to the Kullback-Leibler pseudo-distance, which gives rise to a convex optimization problem. After developing the variational analysis, we discuss the properties of an efficient algorithm for the solution of the corresponding dual problem, based on the iteration of a nonlinear map in a bounded subset of the dual space. Our main result is the proof of local convergence of the latter, established as a consequence of the central manifold theorem. Supported by numerical evidence, we conjecture that, in the mentioned bounded set, the convergence is actually global.
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ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2010.2057171