def optimise_newton(x, a, c, tolerance=0.001):
    """
    Optimise value of x using newton gauss
    """
    x_new = x
    x_old = x-1 # dummy value
    while np.abs(x_new - x_old).sum() > tolerance:
        x_old = x_new
        x_new = newton_update(x_old, a, c)
    return x_new