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March 31, 20260 citationsOpen Access

Triplet-Based Framework for Local Geometry of Polynomial Roots

A Triplet-Based Parameterization for the Local Asymptotic Characterization of Polynomial Roots

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Authors

RBRalf Becker

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Overview

This framework characterizes polynomial roots' geometry in a compact format, suggesting new insights into root dominance.

Key Points

  • The aim is to develop a three-parameter framework that describes the local characteristics of polynomial roots.
  • Introduced a model including position, algebraic multiplicity, and characteristic deflection distance
  • Analyzed the geometric implications of root arrangements and multiplicity
  • Developed symbolic and numerical implementations in Python
  • Found that lower-multiplicity roots can dominate geometrically over higher-multiplicity roots
  • Demonstrated new geometric comparisons across roots of different polynomial degrees
  • The characteristic deflection distance extends the classical condition number for roots of arbitrary multiplicity

Cite This Study

Ralf Becker (2026) studied this question.

synapsesocial.com/papers/69cb650ee6a8c024954b9158https://doi.org/10.5281/zenodo.19303726
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