Fixed-Point Stability Check

Problem

A fixed point x* of x = g(x) is locally attracting when |g'(x*)| < 1.

Given the polynomial coefficients of g(x) = sum(coeffs[i] * x^i) and the fixed point x, return True when the iteration is stable and False otherwise.

Hint

Differentiate g term by term and test the magnitude of the derivative at the point.

case 1

in: [[0,0.5],2]

expected: true

case 2

in: [[0,2],1]

expected: false

case 3

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

expected: true

case 4

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

expected: true

case 5

in: [[0,1,-0.5],0.5]

expected: true

Starter codePython

def fixed_point_stable(coeffs, x):
    # Return True when abs(g'(x)) < 1
    # Your code here
    pass

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