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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Vydáno v:	IEEE transactions on automatic control Ročník 56; číslo 3; s. 506 - 515
Hlavní autoři:	Ferrante, Augusto, Ramponi, Federico, Ticozzi, Francesco
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York, NY IEEE 01.03.2011 Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:	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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Shrnutí:	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.
Bibliografie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 ObjectType-Article-2 ObjectType-Feature-1 content type line 23
ISSN:	0018-9286 1558-2523
DOI:	10.1109/TAC.2010.2057171