Backtracking New Q-Newton's method, Newton's flow, Voronoi's diagram and Stochastic root finding

Autor:	Fornaess, John Erik, Hu, Mi, Truong, Tuyen Trung, Watanabe, Takayuki
Rok vydání:	2024
Předmět:	Mathematics - Optimization and Control Computer Science - Machine Learning Mathematics - Complex Variables Mathematics - Dynamical Systems Mathematics - Numerical Analysis
Druh dokumentu:	Working Paper
Popis:	A new variant of Newton's method - named Backtracking New Q-Newton's method (BNQN) - which has strong theoretical guarantee, is easy to implement, and has good experimental performance, was recently introduced by the third author. Experiments performed previously showed some remarkable properties of the basins of attractions for finding roots of polynomials and meromorphic functions, with BNQN. In general, they look more smooth than that of Newton's method. In this paper, we continue to experimentally explore in depth this remarkable phenomenon, and connect BNQN to Newton's flow and Voronoi's diagram. This link poses a couple of challenging puzzles to be explained. Experiments also indicate that BNQN is more robust against random perturbations than Newton's method and Random Relaxed Newton's method. Comment: 48 pages. Some typos are fixed. Comments are welcome!. arXiv admin note: text overlap with arXiv:2312.12166
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2401.01393 Zobrazit plný text záznamu View this record from Arxiv