created Script for Sekantenverfahren

Schenk_Brandenberger_S5_Aufg1.py

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+import math
+
+import numpy as np
+import matplotlib.pyplot as plt
+
+
+def f(x):
+    return math.pow(math.e, math.pow(x, 2)) + math.pow(x, -3) - 10
+
+
+def f_diff(x):
+    return 2 * x * math.pow(math.pow(math.e, x), 2) - 3 * math.pow(x, -4)
+
+
+def newtonStep(xn, function, function_diff):
+    return xn - (function(xn)) / (function_diff(xn))
+
+def simpleNewtonStep(xn, function, function_diff_x0):
+    return xn - ((function(xn)) / (function_diff_x0))
+
+def secantStep(xn, xn_1, function):
+    return xn - (xn - xn_1)/(function(xn) - function(xn_1)) * f(xn)
+
+def newton(x0, iterations, function, function_diff):
+    print("Newton Verfahren:")
+    x = []
+    x.append(x0)
+    print("x" + str(0) + ":", str(x[0]))
+    for i in range(iterations):
+        x.append(newtonStep(xn=x[i], function=function, function_diff=function_diff))
+        print("x" + str(i + 1) + ":", str(x[i + 1]))
+
+
+
+
+
+if __name__ == '__main__':
+    newton(x0=2, iterations=4, function=f, function_diff=f_diff)
+    simpleNewton(x0=0.5, iterations=4, function=f, function_diff=f_diff)