In this paper, the dynamics of the Chebyshev-Halley family is studied on quadratic polynomials. A singular set, that we call cat set, appears in the parameter space associated to the family. This cat set has interesting similarities with the Mandelbrot set. The parameters space has allowed us to find different elements of the family such that can not converge to any root of the polynomial, sinc...

In this paper, we suggest and analyze a new family of iterative methods for finding zeros of multiplicity of nonlinear equations by using the variational iteration technique. These new methods include the Halley method and its variants forms as special cases. We also give several examples to illustrate the efficiency of these methods. Comparison with modified Newton method is also given. These ...

We present a local convergence analysis of a Modified Halley-Like Method of high convergence order in order to approximate a solution of a nonlinear equation in a Banach space. Our sufficient convergence conditions involve only hypotheses on the first Fréchet-derivative of the operator involved. Earlier studies use hypotheses up to the third Fréchet-derivative [26]. Numerical examples are also ...

Reducing energy consumption is an increasingly important issue in computing and embedded systems. In computing systems, minimizing energy consumption can significantly reduces the amount of energy bills. The demand for computing systems steadily increases and the cost of energy continues to rise. In embedded systems, reducing the use of energy allows to extend the autonomy of these systems. In ...