MediumCalculusca-023

Newton Method n Steps

Problem

Run n iterations of the Newton-Raphson update x = x - f(x) / f'(x) for f(x) = sum(coeffs[i] * x^i), starting from x0.

Return the final iterate. With n = 0 the starting point is returned unchanged.

Hint

Newton's method converges quadratically, so a handful of steps gets very close to the root.

case 1

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

expected: 1.4142156862745099

case 2

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

expected: 1.6363636363636365

case 3

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

expected: 3

case 4

in: [[-9,0,1],1,5]

expected: 3

Starter codePython

def newton_iterate(coeffs, x0, n):
    # Your code here
    pass

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