Interpolation-based methods
- When a step produces an approximate result, you are free to carry it out approximately
Secant iteration:
xk+1=xk−f(xk)(xk−xk−1)f′(xk)−f(xk+1),k=2,3,...
- converges at a rate strictly between linear and quadratic
- if function evaluations are used to measure work, secant iteration converges more rapidly than Newton’s method