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Register a new userGeneralized algorithms for the approximate matrix polynomial GCD of reducing data uncertainties with application to MIMO system and control
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Added by
Antonio Fazzi
Publication date
2019
fields
Informatics Engineering
and research's language is
English
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Computation of (approximate) polynomials common factors is an important problem in several fields of science, like control theory and signal processing. While the problem has been widely studied for scalar polynomials, the scientific literature in the framework of matrix polynomials seems to be limited to the problem of exact greatest common divisors computation. In this paper, we generalize two algorithms from scalar to matrix polynomials. The first one is fast and simple. The second one is more accurate but computationally more expensive. We test the performances of the two algorithms and observe similar behavior to the one in the scalar case. Finally we describe an application to multi-input multi-output linear time-invariant dynamical systems.
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We study a variant of the univariate approximate GCD problem, where the coefficients of one polynomial f(x)are known exactly, whereas the coefficients of the second polynomial g(x)may be perturbed. Our approach relies on the properties of the matrix which describes the operator of multiplication by gin the quotient ring C[x]=(f). In particular, the structure of the null space of the multiplication matrix contains all the essential information about GCD(f; g). Moreover, the multiplication matrix exhibits a displacement structure that allows us to design a fast algorithm for approximate GCD computation with quadratic complexity w.r.t. polynomial degrees.
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