feat: aufgabe 4 abgeschlossen

introduction/serie_2.py

@@ -0,0 +1,49 @@
+#%%
+import numpy as np
+
+# %%
+print("Aufgabe 4")
+
+def fixpunkt_iteration(f, x=1.0, tol=1e-7, N=1000):
+    x_new = f(x)
+    i = 0
+
+    while(np.abs(x_new-x) > tol):
+        if i > N:
+            raise RuntimeError("Keine Konvergenz erreicht")
+
+        x = x_new
+        x_new = f(x)
+        i += 1
+    return [x_new, i]
+
+# Ausgabe
+print("----------------------------------------------------------------------")
+print(__file__)
+print("----------------------------------------------------------------------")
+
+f = lambda x: 1-(1/5)*x
+try:
+    fixpunkt_a, iterationen_a = fixpunkt_iteration(f)
+except RuntimeError as error:
+    print(f"a) f(x) = 1-(1/5)*x\n{error}")
+else:
+    print(f"a) f(x) = 1-(1/5)*x\nFixpunkt: {fixpunkt_a}\nIterationen: {iterationen_a}\n")
+
+f = np.cos
+try:
+    fixpunkt_b, iterationen_b = fixpunkt_iteration(f)
+except RuntimeError as error:
+    print(f"b) f(x) = cos(x)\n{error}")
+else:
+    print(f"b) f(x) = cos(x)\nFixpunkt: {fixpunkt_b}\nIterationen: {iterationen_b}\n")
+
+f = lambda x: np.e**-x
+try:
+    fixpunkt_c, iterationen_c = fixpunkt_iteration(f)
+except RuntimeError as error:
+    print(f"c) f(x) = e⁻x\n{error}")
+else:
+    print(f"c) f(x) = e⁻x\nFixpunkt: {fixpunkt_c}\nIterationen: {iterationen_c}\n")
+
+print("----------------------------------------------------------------------")