Spectral Factorizations and Sums of Squares Representations via Semidefinite Programming
J. W. McLean, Hugo J. Woerdeman · SIAM Journal on Matrix Analysis and Applications · 2002
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.