High-order nonlinear solver for multiple roots

Basins of attraction for Zhou–Chen–Song fourth order family of methods for multiple roots

“…[17,[6][7][8]10,11,13,14,21,24,25,27]. Some of these methods are considered optimal in the sense of Kung and Traub [9], i.e.…”

A sixth-order family of three-point modified Newton-like multiple-root finders and the dynamics behind their extraneous fixed points

“…It is known that numerical scheme (1.1) is a second-order one-point optimal [23] method on the basis of Kung-Traub's conjecture [23] that any multipoint method [35] without memory can reach its convergence order of at most 2 r−1 for r functional evaluations. We can find other higher-order multiple-zero finders in a number of literatures [16][17][18]21,24,25,31,32,40,45] .…”

Comparing the basins of attraction for Kanwar–Bhatia–Kansal family to the best fourth order method

“…a method of order 1.5 [5], a method of order 2 [6], third order methods [7][8][9][10][11][12][13][14][15][16][17], and [18]. The fourth order methods [19][20][21][22][23] and [24]. Some of these methods are considered optimal in the sense of Kung and Traub [25], i.e.…”