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exercise-2.py
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exercise-2.py
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import math
from tabulate import tabulate
def f(x):
return math.pow(x, 3) + 0.4 * math.pow(x, 2) + 0.6 * x - 1.6
def fd(x):
return 3 * math.pow(x, 2) + 0.8 * x + 0.6
def solve_newton(a, b, epsilon=0.001):
table = []
i = 0
x = b
while True:
i += 1
n_x = x - f(x) / fd(x)
delta = round(abs(n_x - x), 3)
table.append([i - 1, round(x, 3), round(f(x), 3), round(fd(x), 3), round(-1 * (f(x) / fd(x)), 3)])
if delta <= epsilon:
break
x = n_x
return table
def solve_hord(a, b, epsilon=0.001):
table = []
i = 0
x = a
while True:
i += 1
n_x = x - f(x) / (f(b) - f(x)) * (b - x)
delta = round(abs(n_x - x), 3)
table.append([
i - 1,
round(x, 3),
round(f(x) / (f(b) - f(x)), 3),
round((b - x), 3)
])
if delta <= epsilon:
break
x = n_x
return table
newton_r = solve_newton(0, 1, 0.001)
print('Ньютон', '\n', tabulate(newton_r, headers=['i', 'x_n', 'f(x_n)', 'fd(x_n)', '-1 * (f(x) / fd(x))']), '\n')
hord_r = solve_hord(0, 1, 0.001)
print('Хорд', '\n', tabulate(hord_r, headers=['i', 'x_n', '(f(x_n) / (f(b) - f(x_n)))', '(b - x_n)']), '\n')