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An iterative method for matrix spectral factorization. (English) Zbl 0748.65041
The factorization problem of a matrix \(H(e^{j\theta})\) is considered, where \(H(e^{j\theta})\) is Hermitian positive definite on \([-\pi,\pi]\) and belongs to the ring of absolutely convergent Fourier series; a spectral factorization has the form \(H(e^{j\theta})=F(e^{j\theta})WF^*(e^{j\theta})\), with \(F(e^{j\theta})=I+\sum^ \infty_{k=1}F_ ke^{j\theta k}\) and \(W>0\).
A numerical algorithm is developed to factorize a multivariate spectrum at a discrete number of frequencies, using an iterative causal projection procedure computed with the aid of the fast Fourier transform.
A benchmark example and an application arising in the control of a pilot scale packed bed reactor are presented to illustrate the method and to emphasize the advantages of the proposed algorithm in comparison with the parametric method which involves a Bauer-type factorization.

MSC:
65F30 Other matrix algorithms (MSC2010)
15A54 Matrices over function rings in one or more variables
15A23 Factorization of matrices
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