De Terán, F., Dopico, F.M. and Pérez, J. (2014) New Bounds for Roots of Polynomials Based on Fiedler Companion Matrices. Linear Algebra and Its Applications, 451, 197-230.
https://doi.org/10.1016/j.laa.2014.03.013

has been cited by the following article:

• TITLE: Bounds for Polynomial’s Roots from Fiedler and Sparse Companion Matrices for Submultiplicative Matrix Norms

  AUTHORS: Mamoudou Amadou Bondabou, Ousmane Moussa Tessa, Amidou Morou

  KEYWORDS: Fiedler Matrices, Polynomial’s Roots, Bounds for Polynomials, Companion Matrices, Sparse Companion Matrices, Hessenberg Matrices, Submultiplicative Matrix Norm

  JOURNAL NAME: Advances in Linear Algebra & Matrix Theory, Vol.11 No.1, February 24, 2021

  ABSTRACT: We use submultiplicative companion matrix norms to provide new bounds for roots for a given polynomial P(X) over the field C[X]. From a n×n Fiedler companion matrix C, sparse companion matrices and triangular Hessenberg matrices are introduced. Then, we identify a special triangular Hessenberg matrix Lr, supposed to provide a good estimation of the roots. By application of Gershgorin’s theorems to this special matrix in case of submultiplicative matrix norms, some estimations of bounds for roots are made. The obtained bounds have been compared to known ones from the literature precisely Cauchy’s bounds, Montel’s bounds and Carmichel-Mason’s bounds. According to the starting formel of Lr, we see that the more we have coefficients closed to zero with a norm less than 1, the more the Sparse method is useful.