FIXED-POINT QUASI-NEWTON METHODS

This article studies iterative methods defined by x(k+1) = PHI(x(k), E(k)), where X(k) is-an-element-of R(n) and E(k) lie on a space of parameters. Sufficient conditions are established for local convergence and for convergence at an ideal linear or superlinear rate. A theory of least-change secant update methods for this class of processes is developed. Several examples are given showing a wide range of applications of the new theory.