ABSTRACT
With all its attractive properties, Ulm’s method (2.1) has a serious shortcoming: the derivative f ′(x) has to be evaluated at each iteration. This makes it inapplicable to equations with nondifferentiable operators and in situations when evaluation of the derivative is too costly. Nondifferentiable operators arise each time the operator f under consideration is defined not on the whole space X, but on some proper subset D ⊂ X of it and so each new iteration x+ generated by an iterative method must belong to this subset. Clearly, no general iterative method can satisfy this requirement. A natural way to deal with the problem is to force x+ onto D (for example, by metric projection) before evaluating f(x+). In other words, the operator f must be globalized to make it suitable for application of a general iterative method. Even differentiable operators most likely become nondifferentiable after their globalization.
