To complement the property of Q-order of convergence we introduce the notions of Q-superorder and Q-suborder of convergence. A new definition of exact Q-order of convergence given in this note generalizes one given by Potra. The definitions of exact Q-superorder and exact Q-suborder of convergence are also introduced. These concepts allow the characterization of any sequence converging with Q-o...

In this paper, we have obtained three optimal order Newton’s like methods of four, eight, and sixteen for solving nonlinear algebraic equations. The convergence analysis all the is discussed separately. We corresponding conjugacy maps quadratic polynomials also extraneous fixed points. considered several test functions to examine explain dynamics our proposed methods. Theoretical results, numer...

Based on Newton’s method, we present a family of three-point iterative methods for solving nonlinear equations. In terms of computational cost, the family requires four function evaluations and has convergence order eight. Therefore, it is optimal in the sense of Kung–Traubhypothesis andhas the efficiency index1.682which is better than that ofNewton’s and many other higher order methods. Some n...

Theobjective in this paper to study and present a new iterative method possessing high convergence order for calculating the polar decompostion of a matrix. To do this, it is shown that the new scheme is convergent and has high convergence. The analytical results are upheld via numerical simulations and comparisons.