MediumCalculusca-208

Damped Newton Step

Problem

A damped (Levenberg-Marquardt style) Newton step solves (H + lambda*I) d = g and moves x_new = x - d.

For the point (x, y), gradient (g1, g2), Hessian [[ha, hb], [hb, hc]], and damping lambda >= 0, return the updated point.

Hint

Adding lambda*I shrinks the step and makes the system better conditioned.

case 1

in: [[0,0],1,1,1,0,1,0]

expected: [-1,-1]

case 2

in: [[0,0],1,1,1,0,1,1]

expected: [-0.5,-0.5]

case 3

in: [[1,1],2,2,2,0,2,0]

expected: [0,0]

case 4

in: [[2,-1],0,0,1,0,1,0]

expected: [2,-1]

Starter codePython

def damped_newton_step(point, g1, g2, ha, hb, hc, lam):
    # Return the updated [x, y]
    # Your code here
    pass

4 test cases · run your code against them in the editor