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feat: newton verfahren für cos funktion

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This commit is contained in:
Sandro Zimmermann 2026-04-09 14:43:02 +02:00
parent a83a731cdc
commit 59149464c4
1 changed files with 7 additions and 3 deletions
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10
src/optimierung/allgemeiner_newton_verfahren.py
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@ -8,7 +8,8 @@ N = 200
x = sp.Symbol("x")
# Funktion
f_sym = x**4 - 10 * x**2 + x
# f_sym = x**4 - 10 * x**2 + x
f_sym = -sp.cos(2 * sp.pi * x)
# Ableitungen
f = sp.lambdify(x, f_sym, "numpy")
@ -16,7 +17,8 @@ f_prime = sp.lambdify(x, sp.diff(f_sym, x), "numpy")
f_second = sp.lambdify(x, sp.diff(f_sym, x, 2), "numpy")
# Daten
x_data = np.linspace(-4, 4, N)
# x_data = np.linspace(-4, 4, N)
x_data = np.linspace(-3, 3, N)
f_data = f(x_data)
# Plot
@ -29,11 +31,12 @@ plt.show()
# Newton Verfahren
# Startwert
startwerte = [0.1]
startwerte = [0.01, 0.02, 0.05, 0.1, 0.2, 0.23, 0.24, 0.245, 0.248, 0.249, 0.2499]
# Iterationsformel
x_n = lambda x: x - f_prime(x) / np.abs(f_second(x))
print(60 * "-")
# Iteration
for x_0 in startwerte:
n = 0
@ -51,4 +54,5 @@ for x_0 in startwerte:
f_x_second = f_second(x_i)
print(f"x_{n}: {x_i}\nf'(x_{n}): {f_x_prime}\nf''(x_{n}): {f_x_second}\n")
limit -= 1
print(60 * "-")
# %%