Numerical solution of positive sum exponential equations (Q1262090)

Let \(F: {\mathbb{R}}^ n\to {\mathbb{R}}^ n\) be a differentiable mapping. In principle, the trajectory of the initial value problem \(F'(x)dx/dt=- F(a),\quad x(0)=a\) provides the solution of \(F(x)=0\) at \(t=1.\) This continuous version of Newton's method is discussed in the first paper. In the second one it is applied to Prony's method for the interpolation of 2n equidistant data by sums of exponentials. The authors observe that the inherent instability of the method (problem?) cannot be overcome by the continuation method.