Fast and backward stable computation of roots of polynomials, Part IIa: general backward error analysis
Year: 2017
Type: report
Abstract: This report is a continuation of "Fast and backward stable computation of roots of polynomials" by J. L. Aurentz, T. Mach, R. Vandebril, and D.S. Watkins, SIAM Journal on Matrix Analysis and Applications, 36(3): 942--973, 2015. It is also an early version of the paper "Fast and backward stable computation of roots of polynomials, Part II: backward error analysis; companion matrix and companion pencil", which we have submitted for publication. We introduce a companion QZ algorithm that computes the roots of a polynomial by solving a generalized eigenvalue problem for a companion pencil. More importantly, we provide an improved backward error analysis that exploits the special structure of the companion matrix or pencil. This report is nearly identical to the paper that we eventually submitted, except for the backward error analysis in Section 5.
Source: Lirias
Authors: Aurentz, Jared L., Mach, Thomas, Robol, Leonardo, Vandebril, Raf, Watkins, David S.
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: KU Leuven
Award: G7099780398
OpenAlex ID: W7019256137