medium · Quantitative Finance numerical
A 'vanishing derivative' (f'(x_n) ≈ 0) in Newton's method often leads to which undesirable outcome?
- The method automatically begins to fall back on Bisection method logic in order to bracket the root instead.
- The observed order of convergence increases further to compensate for the vanishing local slope near the current point.
- The next guess x_n+1 is projected to a point very far from the current region, potentially leading to divergence.
- The algorithm converges prematurely onto a local minimum of the objective function and halts before ever locating an actual root.
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