A CMV--based eigensolver for companion matrices

Abstract

In this paper we present a novel matrix method for polynomial rootfinding. By exploiting the properties of the QR eigenvalue algorithm applied to a suitable CMV-like form of a companion matrix we design a fast and computationally simple structured QR iteration.

14 pages, 4 figures

References in corpus (3)

• The uniqueness in the inverse problem for transmission eigenvalues for the spherically-symmetric variable-speed wave equation
• Compression of unitary rank--structured matrices to CMV-like shape with an application to polynomial rootfinding
• Implicit QR for Companion-like Pencils

Cited by in corpus (4)

• On The Space-Time Fractional Schrödinger Equation with time independent potentials
• Fast and backward stable computation of roots of polynomials, Part II: backward error analysis; companion matrix and companion pencil
• Orthogonal iterations on Structured Pencils
• Fast Hessenberg reduction of some rank structured matrices