week 11


Gradient descent methods. Step size choices. Backtracking rule.

Newton algorithm. Solving systems of nonlinear equations. Quadratic convergence,

Sample problems

  • Compute first 5 iterations \(x_0=2,x_1,\ldots, x_5 \) of Newton method to solve

    Plot \(\log|x_k^2-5|\).

  • For \(x_0\) close to \(0\) the iterations of Newton method to solve
    quickly converge to \(0\) (what else!?). Find the largest interval where this is true (i.e. find the smallest \(x_0>0\) starting with which the iterations of the Newton method fail to converge).
No comments yet.

Leave a Reply