Function newton

solutions.py:268–304

Calculate the root of an equation by the Newton method. Args: f (function): equation f(x). df (function): derivative of quation f(x). x0 (float): initial guess. toler (float): tolerance (stopping criterion). iter_max (int): maximum number of iterations (s

(f, df, x0, toler, iter_max)

def newton(f, df, x0, toler, iter_max):
    """Calculate the root of an equation by the Newton method.

    Args:
        f (function): equation f(x).
        df (function): derivative of quation f(x).
        x0 (float): initial guess.
        toler (float): tolerance (stopping criterion).
        iter_max (int): maximum number of iterations (stopping criterion).

    Returns:
        root (float): root value.
        iter (int): number of iterations used by the method.
        converged (boolean): flag to indicate if the root was found.
    """
    fx = f(x0)
    dfx = df(x0)
    x = x0

    print(f"i = 000,\tx = {x:+.4f},\tfx = {fx:+.4f}")

    converged = False
    for i in range(1, iter_max + 1):
        delta_x = -fx / dfx
        x += delta_x
        fx = f(x)
        dfx = df(x)

        print(f"i = {i:03d},\tx = {x:+.4f},\t", end="")
        print(f"fx = {fx:+.4f},\tdx = {delta_x:+.4f}")

        if math.fabs(delta_x) <= toler and math.fabs(fx) <= toler or dfx == 0:
            converged = True
            break

    root = x
    return root, i, converged