An Approximate Decomposition of a Multivariate Polynomial Based on Structured Low-Rank Approximation
Year: 2026
Type: article
Abstract: A multivariate polynomial $f$ is decomposable if $f$ is a composition $f=u\circ h$ , where $u$ is a univariate polynomial of degree greater than one and $h$ is a multivariate polynomial. We consider the problem of computing the nearest decomposable polynomial to a given multivariate polynomial with respect to the 2-norm. By using the relationship between the decomposability of a polynomial and the rank of a structured matrix corresponding to the polynomial, we reduce this problem to the structured low-rank approximation problem. Then we propose algorithms for computing an approximate decomposition of a multivariate polynomial based on the structured low-rank approximation problem.
Source: Mathematics in Computer Science
Authors: Rikuna Tokuda, Hiroshi Sekigawa
Institution: Tokyo University of Science
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,290
OpenAlex ID: W7225332326