Solved Task 1a

Schenk_Brandenberger_S4_Aufg1.py

@@ -0,0 +1,40 @@
+import math
+import time
+
+import numpy as np
+import matplotlib.pyplot as plt
+
+def F(x):
+    return (230 * math.pow(x, 4) + 18 * math.pow(x, 3) + 9 * math.pow(x, 2) - 9) / 221
+
+def FDiff(x):
+    return (920 * math.pow(x, 3) + 54 * pow(x, 2) + 18 * x) / 221
+
+
+def calcAlpha(start, stop, FDiff):
+    x = np.arange(start, stop + abs(((start-stop)/100)), abs(((start-stop)/100)))
+    y = [FDiff(x_value) for x_value in x]
+    ymax = max(y)
+    return ymax
+
+def iteration(x0, startValue, endValue, function, functionDiff, maxFehler):
+    alpha = calcAlpha(startValue, endValue, functionDiff)
+    print("alpha", alpha)
+    x = [x0]
+    n = 0
+    while(True):
+        time.sleep(1)
+        n = n + 1
+        x.append(function(x[n-1]))
+        print("n:", n, "x:", x[n])
+        fehlerabschatzung = abs(x[n] - x[n - 1]) # math.pow(alpha, n) / (1 - alpha)) *
+        print("fehlerabschatzung", fehlerabschatzung)
+        if(fehlerabschatzung < maxFehler):
+            print("n: ", n)
+            return x[n]
+
+
+if __name__ == '__main__':
+    result = iteration(x0=-0.1, startValue=-1, endValue=0, function=F, functionDiff=FDiff, maxFehler=math.pow(10, -6))
+    #result = iteration(x0=-1, startValue=0, endValue=1, function=F, functionDiff=FDiff, maxFehler=math.pow(10, -6))
+    print(result)