Computing Simple Roots by an Optimal Sixteenth-Order Class

Computing Simple Roots by an Optimal Sixteenth-Order Class

The problem considered in this paper is to approximate the simple zeros of the function f x by iterative processes. An optimal 16th order class is constructed. The class is built by considering any of the optimal three-step derivative-involved methods in the first three steps of a four-step cycle in which the first derivative of the function at the fourth step is estimated by a combination of a...

Optimal Sixteenth Order Convergent Method Based on Quasi-Hermite Interpolation for Computing Roots

We have given a four-step, multipoint iterative method without memory for solving nonlinear equations. The method is constructed by using quasi-Hermite interpolation and has order of convergence sixteen. As this method requires four function evaluations and one derivative evaluation at each step, it is optimal in the sense of the Kung and Traub conjecture. The comparisons are given with some ot...

Computing an Optimal Contract in Simple Technologies

We study an economic setting in which a principal motivates a team of strategic agents to exert costly effort toward the success of a joint project. The action taken by each agent is hidden and affects the (binary) outcome of the agent’s individual task stochastically. A Boolean function, called technology, maps the individual tasks’ outcomes into the outcome of the whole project. The principal...

A Sixteenth-order Polylogarithm Ladder

New optimal class of higher-order methods for multiple roots, permitting f′(xn) = 0

Finding multiple zeros of nonlinear functions pose many difficulties for many of the iterative methods. A major difficulty in the application of iterative methods is the selection of initial guess such that neither guess is far from zero nor the derivative is small in the vicinity of the required root, otherwise the methods would fail miserably. Finding a criterion for choosing initial guess is...