2019/05/10 by Fredy Vides, Vides, Fredy
Computer Science · Engineering · Mathematics · Physics and Astronomy · #47N70 (primary) and 93C57 #93B25 (secondary) #93B28 #Control Systems and Identification #Dynamical Systems (math.DS) #FOS: Mathematics #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Numerical methods for differential equations #Operator Algebras (math.OA) #cs.NA #math.DS #math.NA #math.OA #msc:47N70 #msc:93B25 #msc:93B28 #msc:93C57
paper · pdf · doi:10.48550/arxiv.1905.03910
openalex publication_date 2019/05/10 · arxiv created 2019/06/12 · arxiv updated 2019/06/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this document the author proves that several problems in data-driven numerical approximation of dynamical systems in ℂn, can be reduced to the computation of a family of constrained matrix representations of elements of the group algebra ℂ[ℤ/m] in ℂn× n, factoring through the commutative algebra Circ(m) of circulant matrices in ℂm× 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.