Bounds for the maximum modulus of polynomial roots with nearly optimal worst-case overestimation

2024/11/25 by Prashant Batra, Batra, Prashant
Computer Science · Mathematics · #12D10 #15A18 #65H04 #Advanced Differential Equations and Dynamical Systems #Algebraic and Geometric Analysis #FOS: Mathematics #Numerical Analysis (math.NA) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2411.16385

openalex publication_date 2024/11/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Many upper bounds for the moduli of polynomial roots have been proposed but reportedly assessed on selected examples or restricted classes only. Regarding quality measured in terms of worst-case relative overestimation of the maximum root-modulus we establish a simple, nearly optimal result.

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