feat: allgemeiner newton verfahren

src/optimierung/allgemeiner_newton_verfahren.py

@@ -0,0 +1,54 @@
+# %%
+import numpy as np
+import sympy as sp
+import matplotlib.pyplot as plt
+
+# Parameter
+N = 200
+x = sp.Symbol("x")
+
+# Funktion
+f_sym = x**4 - 10 * x**2 + x
+
+# Ableitungen
+f = sp.lambdify(x, f_sym, "numpy")
+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)
+f_data = f(x_data)
+
+# Plot
+plt.figure(1)
+plt.plot(x_data, f_data)
+plt.xlabel("x")
+plt.ylabel("y")
+plt.grid("on")
+plt.show()
+
+# Newton Verfahren
+# Startwert
+startwerte = [0.1]
+
+# Iterationsformel
+x_n = lambda x: x - f_prime(x) / np.abs(f_second(x))
+
+# Iteration
+for x_0 in startwerte:
+    n = 0
+    x_i = x_0
+    f_x_prime = f_prime(x_0)
+    f_x_second = f_second(x_0)
+    print(f"x_{n}: {x_0}\nf'(x_{n}): {f_x_prime}\nf''(x_{n}): {f_x_second}\n")
+
+    limit = 1000
+
+    while np.abs(f_x_prime) > 1e-10 and limit > 0:
+        n += 1
+        x_i = x_n(x_i)
+        f_x_prime = f_prime(x_i)
+        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
+# %%

src/optimierung/newton_verfahren.py

@@ -92,7 +92,7 @@ for x_0 in startwerte:
     f_x_prime = f_prime(x_0)
     print(f"x_{n}: {x_0}\nf'(x_{n}): {f_x_prime}\n")
 
-    limit = 4
+    limit = 1000
 
     while np.abs(f_x_prime) > 1e-16 and limit > 0:
         n += 1