Spectral factorizations and sums of squares representations via semidefinite programming

Spectral factorizations and sums of squares representations via semidefinite programming

In this paper we find a characterization for when a multivariable trigonometric polynomial can be written as a sum of squares. In addition, the truncated moment problem is addressed. A numerical algorithm for finding a sum of squares representation is presented as well. In the one-variable case, the...

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Veröffentlicht in:SIAM journal on matrix analysis and applications 2002, Vol.23 (3), p.646-655
Hauptverfasser: MCLEAN, J. W, WOERDEMAN, H. J
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Algorithms
Applied sciences
Computer science
control theory
systems
Control theory. Systems
Exact sciences and technology
Fourier analysis
Hilbert space
Linear and multilinear algebra, matrix theory
Mathematical analysis
Mathematics
Sciences and techniques of general use
Semidefinite programming
System theory
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Zusammenfassung:In this paper we find a characterization for when a multivariable trigonometric polynomial can be written as a sum of squares. In addition, the truncated moment problem is addressed. A numerical algorithm for finding a sum of squares representation is presented as well. In the one-variable case, the algorithm finds a spectral factorization. The latter may also be used to find inner-outer factorizations.
ISSN:0895-4798
1095-7162
DOI:10.1137/S0895479800371177