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On the Convergence of an Efficient Algorithm for Kullback–Leibler Approximation of Spectral Densities.
- Source :
- IEEE Transactions on Automatic Control; 03/01/2011, Vol. 56 Issue 3, p506-515, 10p
- Publication Year :
- 2011
-
Abstract
- 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00189286
- Volume :
- 56
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- IEEE Transactions on Automatic Control
- Publication Type :
- Periodical
- Accession number :
- 59195767
- Full Text :
- https://doi.org/10.1109/TAC.2010.2057171