A stable algorithm to compute the roots of polynomials is presented. The roots are found by
computing the eigenvalues of the associated companion matrix by Francis's implicitly shifted …

The numerical method of Helsing and co-workers evaluates Laplace and related layer
potentials generated by a panel (composite) quadrature on a curve, efficiently and with high …

Core-Chasing Algorithms for the Eigenvalue Problem : Back Matter Page 1 Bibliography [1] GS
Ammar, WB Gragg, and L. Reichel. On the eigenproblem for orthogonal matrices. In Proceedings …

This work is a continuation of work by JL Aurentz, T. Mach, R. Vandebril, and DS Watkins, J.
Matrix Anal. Appl., 36 (2015), pp. 942--973. In that paper we introduced a companion QR …

A common way of computing the roots of a polynomial is to find the eigenvalues of a
linearization, such as the companion (when the polynomial is expressed in the monomial …

In this paper we present a novel matrix method for polynomial rootfinding. We approximate
the roots by computing the eigenvalues of a permuted version of the companion matrix …

The analysis of any Hessenberg matrix as a product of a companion matrix and a triangular
matrix is presented in this paper. The factors are explicitly given on terms of the entries of the …

The class of sparse companion matrices was recently characterized in terms of unit
Hessenberg matrices. We determine which sparse companion matrices have the lowest …

In this paper we present a new decomposition of the tridiagonal matrices using the CL
factorization to calculate the inverse of these matrices. And we suggest, two algorithms to …

[16] P.-A. Absil, R. Mahony, and B. Andrews. Convergence of the iterates of descent
methods for analytic cost functions. SIAM J. Optim., 16 (2): 531–547, 2005.[17] A. Abu-Omar …