Seventh-order iterative algorithm free from second derivative for solving algebraic nonlinear equations

In this paper, we introduce an iterative algorithm free from second derivative for solving algebraic nonlinear equations. The analysis of convergence shows that this iterative algorithm has seventh order convergence. Per iteration of the new algorithm requires three evaluations of the function and two evaluation of its rst derivative. Therefore this algorithm has the eciency index which equals to 1.477. The results obtained using the algorithm presented here show that the iterative algorithm is very eective and convenient for the algebraic nonlinear equations.