2020/08/04 by Andrii Dmytryshyn, Dmytryshyn, Andrii
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.2008.01794
openalex publication_date 2020/08/04 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
A number of theoretical and computational problems for matrix polynomials are\nsolved by passing to linearizations. Therefore a perturbation theory results\nfor linearizations need to be related back to matrix polynomials. In this paper\nwe present an algorithm that finds which perturbation of matrix coefficients of\na matrix polynomial corresponds to a given perturbation of the entire\nlinearization pencil. Moreover we find transformation matrices that, via strict\nequivalence, transform a perturbation of the linearization to the linearization\nof a perturbed polynomial. For simplicity, we present the results for the first\ncompanion linearization but they can be generalized to a broader class of\nlinearizations.\n