On recurrence relations arising from NRS(2) applied to a cubic polynomial
Abstract
We prove that the leading coefficient of the "error" terms of NRS(2) applied to a cubic polynomial $f(z)$ with starting point $(-\frac{a_1}{a_2}, -\frac{a_1}{a_2})$ are positive-coefficient rational functions in the zeros of $f(z)$. We express these terms as a sum over combinatorial objects which we call radius-value trees.
Fields of Study & Subjects
Mathematical functions and polynomials
Polynomial and algebraic computation
Advanced Combinatorial Mathematics
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 13 February 2026
- Language
- EN
- Document type
- Preprint