MediumCalculusca-116

Newton for 2x2 System One Step

Problem

Take one Newton step for the system f1 = x^2 + y^2 - 25 = 0 and f2 = x - y - 1 = 0.

The Jacobian is [[2x, 2y], [1, -1]]. Solve J * [dx, dy] = -[f1, f2] with Cramer's rule and return the updated point [x + dx, y + dy].

Hint

Evaluate f and J at the current point, then solve the 2x2 linear system.

case 1

in: [[3,4]]

expected: [4.142857142857142,3.142857142857143]

case 2

in: [[4,3]]

expected: [4,3]

case 3

in: [[5,0]]

expected: [5,4]

case 4

in: [[1,1]]

expected: [7.25,6.25]

Starter codePython

def newton_system_2x2(point):
    # Your code here
    pass

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