On the Vykhandu-Levin iterative method for numerical solution of nonlinear systems (Q1919497)

The main purpose of this paper is to show that the Vykhandu-Levin method, which is briefly derived, converges only quadratically. It was originally claimed that the method is of cubic convergence rate, but there was a flaw in the argument as one of the assumed conditions can not be satisfied. The proof also shows that early observations on faster than quadratic convergence in the univariate case were correct, as here the one obtains cubic convergence.