Work

A General Approach to Error Analysis for Roots of Polynomial Equations

Year: 2025

Type: article

Abstract: We study equations with real polynomials of arbitrary degree, such that each coefficient has a small, individual error; this may originate, for example, from imperfect measuring. In particular, we study the influence of the errors on the roots of the polynomials. The errors are modeled by imprecisions of Sorites type: they are supposed to be stable to small shifts. We argue that such imprecisions are appropriately reflected by (scalar) neutrices, which are convex subgroups of the nonstandard real line; examples are the set of infinitesimals, or the set of numbers of order ε, where ε is a fixed infinitesimal. The Main Theorem states that the imprecisions of the roots are neutrices, and determines their shape.

Source: AppliedMath

DOI: 10.3390/appliedmath5030120

Authors: Imme van den Berg, João Carlos Lopes Horta

Institutions: University of Évora, Centro de Investigação em Matemática e Aplicações, University of Cape Verde

Language: English

Topic: Mathematical and Theoretical Analysis

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,207

OpenAlex ID: W4413990612

FWCI:

Cites: 18

Cited by:

Related to: 10