A nonlinear equation f (x)= 0 is mathematically transformed to a coupled system of quasi-
linear equations in the two-dimensional space. Then, a linearized approximation renders a …

Starting by King's method, we propose a modified families of fourth-and eighth-order of
convergence iterative methods for nonlinear equations. The fourth-order method requires at …

We present a local convergence analysis of a derivative free fourth order method with one
parameter based on rational interpolation in order to approximate a locally unique root of a …

We construct a family of derivative‐free optimal iterative methods without memory to
approximate a simple zero of a nonlinear function. Error analysis demonstrates that the …

This study explored the convergence rate of the hybrid numerical iterative technique (HNIT)
for the solution of nonlinear problems (NLPs) of one variable (f (x)= 0). It is sightseen that …

Finding a simple root for a nonlinear equation f (x)= 0, f: I⊆ R→ R has always been of much
interest due to its wide applications in many fields of science and engineering. Newton's …

Based on the two-point Hermite interpolation technique, the paper proposes a two-point
generalized Hermite interpolation and its inversion in terms of weight functions. We prove …

The most popular financial yardstick of investment productivity is the Internal Rate of Return
(IRR). The fastest way to calculate IRR is by using iterative root-finding algorithms, the most …

In this paper, a general procedure to develop some four-parametric with-memory methods to
find simple roots of nonlinear equations is proposed. The new methods are improved …

In this manuscript, we construct a general family of optimal derivative free iterative methods
by using rational interpolation. This family is further extended to a family of with-memory …