PreprintCC BY-NC-ND 4.0arXiv
The paxotopy method for finding isolated roots of a system of nonlinear equations
Abstract
We focus on systems of nonlinear equations, where some equations are non-polynomial. Building on the remarkable developments in solving polynomial systems during the recent decades, and on a few extensions to specific examples of the transcendental case, a general framework for finding isolated roots is proposed. The name paxotopy is proposed after (1) Polynomial ApproXimation of the transcendental functions, then (2) solving the approximating polynomial system by the homOTOPY continuation method, and finally (3) the roots of the polynomial systems are used as starting points of a Newton's iteration to arrive at the solutions of the original system. These steps combine the advantages of local and global methods.
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BibTeX
@misc{bozoki2026paxotopy,
title = {{The paxotopy method for finding isolated roots of a system of nonlinear equations}},
author = {Sándor Bozóki},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.34583},
eprint = {2609.34583},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.34583},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - The paxotopy method for finding isolated roots of a system of nonlinear equations
AU - Sándor Bozóki
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.34583
UR - https://arxiv.org/abs/2609.34583
AB - We focus on systems of nonlinear equations, where some equations are non-polynomial. Building on the remarkable developments in solving polynomial systems during the recent decades, and on a few extensions to specific examples of the transcendental case, a general framework for finding isolated roots is proposed. The name paxotopy is proposed after (1) Polynomial ApproXimation of the transcendental functions, then (2) solving the approximating polynomial system by the homOTOPY continuation method, and finally (3) the roots of the polynomial systems are used as starting points of a Newton's iteration to arrive at the solutions of the original system. These steps combine the advantages of local and global methods.
ER -