Polynomial Root-finding via Structured Matrices

par Esteban Segura Ugalde (Université de Limoges ; CNRS XLIM UMR 6172 - DMI)

jeudi 3 nov. 2011, 10:30 → 11:30 Europe/Paris

XR.203 (Bâtiment XLIM)

We study the problem of approximating the zeros of an univariate polynomial (up to machine precision). Some popular iterative root-finding methods construct companion matrices (Frobenius, Lagrange) associated with the given polynomial and use eigensolvers to find the eigenvalues of such matrices. Our goal is to study this root-finding technique, exploiting the structure (e.g., diagonal plus rank one) of companion matrices to obtain a decrease of computational cost and memory requirements.