Newton-like methods for the computation of fixed points

AbstractThe celebrated Banach fixed point theorem provides conditions which assure that the method of successive substitution is convergent; the convergence, however, may take place very slowly so that it may be desirable to use a Newton-like method for the computation of the fixed point. If Newton's method itself is applied one ignores the additional information that the problem arises from a frixed point problem with a contraction mapping. In the present note some variants of Newton's method are discussed which make use of this contraction information; it turns out that the convergence of Newton's method can be accelerated without any relevant additional computational labour