feat: Heron Verfahren implementiert

introduction/serie_2.py

@@ -1,14 +1,15 @@
-#%%
+# %%
 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):
+    while np.abs(x_new - x) > tol:
         if i > N:
             raise RuntimeError("Keine Konvergenz erreicht")
 
@@ -17,18 +18,21 @@ def fixpunkt_iteration(f, x=1.0, tol=1e-7, N=1000):
         i += 1
     return [x_new, i]
 
+
 # Ausgabe
 print("----------------------------------------------------------------------")
 print(__file__)
 print("----------------------------------------------------------------------")
 
-f = lambda x: 1-(1/5)*x
+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")
+    print(
+        f"a) f(x) = 1-(1/5)*x\nFixpunkt: {fixpunkt_a}\nIterationen: {iterationen_a}\n"
+    )
 
 f = np.cos
 try:
@@ -47,3 +51,38 @@ else:
     print(f"c) f(x) = e⁻x\nFixpunkt: {fixpunkt_c}\nIterationen: {iterationen_c}\n")
 
 print("----------------------------------------------------------------------")
+
+##%
+# Parameter
+q = 2.0
+a_0 = 1.0
+pr = 16
+
+
+# Funktionen
+def f(x):
+    y = 0.5 * (x + q / x)
+    return y
+
+
+# Iteration
+w = 0.0
+a = a_0
+k = 0
+
+print("----------------------------------------------------------------------")
+print(__file__)
+print("----------------------------------------------------------------------")
+print("Iteration :")
+print(f"a_{k} = {a:#.16g}")
+
+while a != w:
+    w = a
+    k = k + 1
+    a = f(a)
+    print(f"a_{k} = {a:#.16g}")
+
+# Ausgabe :
+print("----------------------------------------------------------------------")
+print(f"Wurzel: sqrt({q:#.{pr}g}) = {a:#.{pr}g}")
+print("----------------------------------------------------------------------")