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math.DS2024
Backtracking New Q-Newton's method for finding roots of meromorphic functions in 1 complex variable: Global convergence, and local stable/unstable curves
John Erik Fornæss, Mi Hu, Tuyen Trung Truong
In this paper, we research more in depth properties of Backtracking New Q-Newton's method (recently designed by the third author), when used to find roots of meromorphic functions.…
math.DS2023
Backtracking New Q-Newton's method, Schröder's theorem, and Linear Conjugacy
John Erik Fornaess, Mi Hu, Tuyen Trung Truong +1
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 perform…
math.DS2023
Orbits inside Fatou sets
John Erik Fornaess, Mi Hu
In this paper, we investigate the precise behavior of orbits inside attracting basins of rational functions on and entire functions in . Let be…