A CMV--based eigensolver for companion matrices
Roberto Bevilacqua, Gianna M. Del Corso, Luca gemignani
TL;DR
This paper introduces a new matrix-based eigensolver for polynomial rootfinding that leverages a CMV-like form of companion matrices and a specialized QR algorithm for improved efficiency.
Contribution
It presents a novel structured QR iteration method tailored for CMV-like forms of companion matrices, enhancing polynomial rootfinding efficiency.
Findings
Achieves faster eigenvalue computation for companion matrices.
Provides a computationally simple and structured QR iteration.
Improves polynomial rootfinding accuracy and speed.
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.
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