2023/01/16 by Miryam Gnazzo, Gnazzo, Miryam, Nicola Guglielmi +1
Computer Science · Mathematics · Physics and Astronomy · #15A18 #47A56 #65K05 #Advanced Mathematical Theories and Applications #Advanced Optimization Algorithms Research #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2301.06335
openalex publication_date 2023/01/16 · openalex created_date 2023/01/19 · openalex updated_date 2026/07/28
Consider a matrix polynomial P ( λ)= A0 + λA1 + … + λd Ad, with A0,…, Ad complex (or real) matrices with a certain structure. In this paper we discuss an iterative method to numerically approximate the closest structured singular matrix polynomial \widetilde P( λ), using the distance induced by the Frobenius norm. An important peculiarity of the approach we propose is the possibility to include different types of structural constraints. The method also allows us to limit the perturbations to just a few matrices and also to include additional structures, such as the preservation of the sparsity pattern of one or more matrices Ai, and also collective-like properties, like a palindromic structure. The iterative method is based on the numerical integration of the gradient system associated with a suitable functional which quantifies the distance to singularity of a matrix polynomial.