Finding the zeros of an analytic function (Q1106625)

The author describes a method for the computation of the zeros of a function f: \({\mathbb{R}}^ n\to {\mathbb{R}}^ n\). His main idea consists in solving the functional equation \(f(z(t))=(1-t)f(a),\) where z(t) denotes a path with \(z(0)=a\), via the initial value problem \(f'(z(t))\cdot \dot z(t)=-f(a),\) \(z(0)=a\). There is no numerical example.