Newton Step for Quadratic 2D

Problem

For f(x) = 0.5 x^T A x - b^T x, the Newton step from x is x_new = x - A^{-1} (A x - b), which reaches the minimizer in one step for a symmetric positive definite A.

Given A as nested rows, b, and x, return the updated point.

Hint

Compute the gradient, invert the 2x2 Hessian, and subtract.

Test cases

case 1

in: [[[2,0],[0,4]],[2,8],[0,0]]

expected: [1,2]

case 2

in: [[[1,0],[0,1]],[1,1],[3,-2]]

expected: [1,1]

case 3

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

expected: [0.3333333333333333,0.3333333333333333]

Starter codePython

def newton_step_quadratic_2d(a, b, x):
    # Your code here
    pass

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