Numerical Methods with Programming

1.

Modify Example 32.2.1 to include the idea of Broyden's method from Example 11.4.1: the script should not use the Hessian matrix fh, instead relying on an approximation to its inverse obtained with Broyden's method. The following modification should help with convergence: start with small initial guess

B = 0.001*eye(2);

and make the stopping condition less restrictive:

norm(h) < 1e-6

Re-run the script several times (about five): since it has a random initial point, the results may differ. Does the minimization process converge to the minimum $(1, 1)$ every time?