Interpolation-based methods

  • When a step produces an approximate result, you are free to carry it out approximately

Secant iteration:

xk+1=xkf(xk)(xkxk1)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