НСАУ. Метод Ньютона и простой итерации

def isNeedToComplete(x_old, x_new, y_old, y_new):
    eps = 1e-5
    sumx_up = 0
    sumx_low = 0
    sumy_up = 0
    sumy_low = 0
    for k in range((0, len(x_old, y_old))):
        sumx_up += (x_new[k] - x_old[k]) ** 2
        sumx_low += (x_new[k]) ** 2
        sumy_up = (y_new[k] - y_old[k]) ** 2
        sumy_low += (y_new[k]) ** 2
 
    return np.sqrt(sumx_up/sumx_low, sumy_up/sumy_low) < eps

def f(x,y):
    return np.tan(x*y)**0.5, ((1-0.7*x*x)/2)**0.5
 
def simple(x, y, eps):
 
    x_old = y_old = np.Inf
    counter = 0
    while max(abs(x_old-x), abs(y_old-y)) > eps:
        x_old, y_old = x, y
        x, y = f(x_old, y_old)
        if max(x,y) >1 or counter > 1000:
            print('Не сошлось')
            return
        counter += 1
 
    print(x,y)
    print(f'{counter} итераций')
    
simple(1,1,1e-5)
simple(0.5,0.5,1e-5)

from math import sqrt, tan
x,y=0.5,0.5
for i in range(10):
    x=tan(sqrt(x*y))
    y=.5-.35*x
    print(sqrt(x),sqrt(y))

import numpy as np
import matplotlib.pyplot as plt
import mplcyberpunk
 
def f2(x):
    return (np.arctan(x * x)) / x
 
def f3(x):
    return ((1 - 0.7 * x * x) / 2) ** 0.5
 
def Newton_sys_graphic():
    fig1, ax = plt.subplots(figsize=(8, 6))
    x = np.linspace(-1, 1, 10)
    plt.ylabel(r'$y$', fontsize=13, fontname='Arial', color='white')
    plt.xlabel(r'$x$', fontsize=13, fontname='Arial', color='white')
    plt.grid(which='both', linewidth=1.5, linestyle='-', color='gray')
    ax.tick_params(which='major', length=8, width=2)
    ax.tick_params(which='minor', length=8, width=2)
    ax.minorticks_on()
    ax.grid(which='major',
            linewidth=2)
    ax.grid(which='minor',
            linestyle=':')
    plt.plot(x, f3(x), x, -f3(x))
    
 
    legend = plt.legend(['Initial approximation'], loc='upper right', shadow=True, fontsize='x-large',
                        frameon=True, title="Легенда", title_fontsize=15, framealpha=1)
    frame = legend.get_frame()
    frame.set_facecolor('black')
    frame.set_edgecolor('red')
    plt.title("Initial approximation")
    mplcyberpunk.add_gradient_fill(alpha_gradientglow=0.5)
    mplcyberpunk.add_glow_effects()
    plt.show()
    fig1.savefig('newton_point.png', dpi=300, bbox_inches='tight')