Singular perturbations arising in complex Newton's method

Authors : Figen Çilingir

Pages : 1172-1178

Doi:10.15672/hujms.1132257

View : 268 | Download : 304

Publication Date : 2023-10-31

Article Type : Research Paper

Abstract :We examine the resulting dynamics when Newton\'s method is applied to perturbations on polynomials that have a multiple root. Specifically, we consider the case where Newton\'s method is applied to the polynomial family $(z^2 + c)(z-1).$
Keywords : Julia set, Newton method, rational iteration, singular perturbations