On a generalization of Steffensen method One of the most important techniques to study nonlinear equations is the Summary: On a generalization of Steffensen method One of the most important techniques to study nonlinear equations is the use of iterative processes, starting from an initial approximation x0, called pivot, successive approaches (until some predetermined convergence criterion is satisŢed) xi are computed , i = 1, 2, . . . , with the help of certain iteration function : X X, xi+1 := (xi), i = 0, 1, 2 . . . (1) Certainly Newton method (second order) is the most useful iteration for this purpose. In this case, we need to evaluate a derivative in each step, it is the main difficulty. Steffensen method (second order) can be considered as a simpliŢcation of original Newton method where F 0 (xk) is replaced by a special approximation. If we are interesting to approximate a solution of the nonlinear equation F (x) = x, (2) Steffensen method can be written as xk+1 = xk + (I - [F(xk), xk; F])-1 (F(xk) - xk). (3) where [·, ·; F] denotes a divided difference of Ţrst order for the operator F : X X (X a Banach space). Collections: Mathematics