Multipoint methods for solving nonlinear equations: A survey

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

“…See, for example, Ostrowski [1], Traub [2], Neta [3] and the recent book by Petković et al [4] and references therein. Zero finders of a scalar function f required in many branches of engineering sciences, physics, computer science, finance, to mention only a few.…”

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

“…(1.1) efficiently locates the desired multiple-root with quadratic-order convergence. 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] .…”

Comparative study of eighth-order methods for finding simple roots of nonlinear equations

“…In fact, we will not discuss derivative-free methods or methods with memory. There are many new methods and families of methods, some of which are just rediscovery of old ones or special cases of known families of methods, see, e.g., [2] for examples of such cases.…”

“…(8) (v) A Hermite interpolation-based eighth-order (HKT8) optimal method based on Kung-Traub fourth-order method (11), see [2], is given by…”

“…(ix) A weight function-based eighth-order (WM8) optimal method [2] using the fourth-order Maheshwari's method ( [30]) is given by…”