On the secant method for solving nonsmooth equations (Q2497389)

The author considers the problem on approximating a locally unique solution of the equation \(F(x)= 0\), where \(F\) is a continuous operator defined on a closed subset \(D\) of a Banach space \(X\) with values in a Banach space \(Y\). A local as well as a semilocal convergence analysis for the secant method is provided using a flexible point-based approximation. The presented results are illustrated by numerical examples.