A note on a modification of Moser's method
We use a recurrence technique to obtain semilocal convergence results for Ulm's iterative method to approximate a solution of a nonlinear equation F(x) = 0 {x(n + 1) = x(n) - B-n F(x(n)), n >= 0, Bn + 1 = 2B(n) - BnF'(x(n + 1)) B-n, n >= 0. This method does not contain inverse operators in its expression and we prove it converges with the Newton rate. We also use this method to approximate a solution of integral equations of Fredholm-type. (C) 2007 Elsevier Inc. All rights reserved.
semilocal convergence iterative processes r-order of convergence