Semilocal convergence of a sixth order iterative method for quadratic equations

Abstract

In this paper the modification of Chebyshevʼs iterative method constructed in Amat et al. (2008) [1] is revisited. The behavior of this method when considering quadratic nonlinear operators is analyzed. In this case, the iterative method has a competitive behavior due to its computational efficiency. Moreover, a new result of semilocal convergence assuming only a pointwise condition is obtained, improving the result given in Amat et al. (2008) [1]. The domain of uniqueness of the solution is also improved. The new technique used in the proof of these results allows us to achieve all these improvements. Finally, some theoretical and numerical applications for a quadratic system of equations are presented.