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A fast solver for the circulant rational covariance extension problem
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
2015 (English)In: 2015 European Control Conference, ECC 2015, Institute of Electrical and Electronics Engineers (IEEE), 2015, 727-733 p.Conference paper (Refereed)Text
Abstract [en]

The rational covariance extension problem is to parametrize the family of rational spectra of bounded degree that matches a given set of covariances. This article treats a circulant version of this problem, where the underlying process is periodic and we seek a spectrum that also matches a set of given cepstral coefficients. The interest in the circulant problem stems partly from the fact that this problem is a natural approximation of the non-periodic problem, but is also a tool in itself for analysing periodic processes. We develop a fast Newton algorithm for computing the solution utilizing the structure of the Hessian. This is done by extending a current algorithm for Toeplitz-plus-Hankel systems to the block-Toeplitz-plus-block-Hankel case. We use this algorithm to reduce the computational complexity of the Newton search from O(n3) to O(n2), where n corresponds to the number of covariances and cepstral coefficients.

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE), 2015. 727-733 p.
Keyword [en]
Bounded degree, Cepstral coefficients, Fast solvers, Hankel systems, Newton algorithm, Periodic problems, Periodic process, Rational covariance extension problem, Control
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-186818DOI: 10.1109/ECC.2015.7330629ScopusID: 2-s2.0-84963853505ISBN: 9783952426937OAI: oai:DiVA.org:kth-186818DiVA: diva2:938601
Conference
European Control Conference, ECC 2015, 15 July 2015 through 17 July 2015
Note

QC 20160617

Available from: 2016-06-17 Created: 2016-05-13 Last updated: 2016-06-17Bibliographically approved

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Ringh, AxelKarlsson, Johan Mikael
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