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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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