On Topologically Controlled Model Reduction for Discrete-Time Systems
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In this document the author proves that several problems in data-driven numerical approximation of dynamical systems in C^n, can be reduced to the computation of a family of constrained matrix representations of elements of the group algebra C[Z/m] in C^n× n, factoring through the commutative algebra Circ(m) of circulant matrices in C^m× m, for some integers m≤ n. The solvability of the previously described matrix representation problems is studied. Some connections of the aforementioned results, with numerical analysis of dynamical systems, are outlined, a prorotypical algorithm for the computation of the matrix representations, and some numerical implementations of the algorithm, will be presented.
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