A new family of methods for nonlinear equations

Abstract

In this paper, a family of seventh-order iterative methods for solving nonlinear equation is presented and analyzed. This family of seventh-order methods contains the Bi's seventh-order methods and many other seventh-order iterative methods as special cases. In terms of computational cost, per iteration the new methods require three evaluations of the function and one evaluation of its first derivative. Therefore their efficiency index is 1.627. The convergence of this family of methods is analyzed to establish its seventh-order convergence. © 2010 Springer-Verlag Berlin Heidelberg.