medium · Quantitative Finance

A 'vanishing derivative' (f'(x_n) ≈ 0) in Newton's method often leads to which undesirable outcome?

1. The method automatically begins to fall back on Bisection method logic in order to bracket the root instead.
2. The observed order of convergence increases further to compensate for the vanishing local slope near the current point.
3. The next guess x_n+1 is projected to a point very far from the current region, potentially leading to divergence.
4. The algorithm converges prematurely onto a local minimum of the objective function and halts before ever locating an actual root.

Sign up free to see the explanation and track your rank →