Consider the Newtons algorithm with Levenberg modification

I. Write a computer sotware that inplements this algorithm. Submit all your code. (4 points) 2. Find a continuous function f : R" R such that the original Newton's algorithm does not converge, but the Levenberg modification works. Verify this using your code. (6 points) 3. Find a function f : Rn ? R such that the neither Newton's algorithm nor Levenberg's modi- fication converges, regardless of how Hk is chosen in Levenberg's modification . Verify using your code. (10 points) I. Write a computer sotware that inplements this algorithm. Submit all your code. (4 points) 2. Find a continuous function f : R" R such that the original Newton's algorithm does not converge, but the Levenberg modification works. Verify this using your code. (6 points) 3. Find a function f : Rn ? R such that the neither Newton's algorithm nor Levenberg's modi- fication converges, regardless of how Hk is chosen in Levenberg's modification . Verify using your code. (10 points)