title: Managing with oscillation and torsion in newton Raphson method without limiting iterations
body: <p>I've been trying to write a MATLAB-function which calculates the a root of a function simply by using Newton-Raphson. The problem with this algorithm is it diverges near torsion points and roots with oscillations (e.g for x^2+2 after 10 iteration with initial guess -1 the method diverges). Is there any satisfying condition to identify when we get oscillations and torsions which doesn't count iterations in a really inefficient way?</p>