On symmetric extraction polynomial matrix spectal factorization
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We report a revision, , of the 1963 Davis algorithm for the spectral factorization of a parahermitian nonnegative polynomial matrix φ by symmetric factor extraction: this algorithm is careless about zeros at infinity. By introducing the notion of diagonal reducedness of φ we obtain an easy sufficient test for the absence of zeros at infinity. We show then i) how to get φ diagonally reduced by diagonal excess reduction steps, removing all zeros at infinity and ii) how to remove symmetrically finite zeros while keeping φ diagonally reduced, (whence free of zeros at infinity). Didactical examples are given. This results in a revised symmetric extraction spectral factorization algorithm with monotone degree control.
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