Newton Step for a Nonlinear System

Problem

For the system f1(x, y) = x^2 + y - 3 and f2(x, y) = x - y^2 + 2, the Jacobian is [[2x, 1], [1, -2y]].

A Newton step is p - J^{-1} F(p). Given the point [x, y], return the updated point. Assume the Jacobian is invertible there.

Hint

Build F and J at the point, invert the 2x2 Jacobian, then subtract J^{-1}F.

case 1

in: [[1,1]]

expected: [1,2]

case 2

in: [[2,0]]

expected: [-2,15]

case 3

in: [[0,2]]

expected: [6,3]

Starter codePython

def newton_step_nonlinear_system(point):
    # Your code here
    pass

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