solved Task 2

Schenk_Brandenberger_S10_Aufg1.py

@@ -0,0 +1,25 @@
+import numpy as np
+
+
+print("*********Jacobi-Verfahren*********")
+def Jacobi(A,b,x,steps):
+    L = np.tril(A,k=-1)
+    D = np.diag(np.diag(A))
+    R = np.triu(A, k=1)
+    for steps in range(steps):
+        x = -np.linalg.inv(D) @ (L + R) @ x + np.linalg.inv(D) @ b
+    #print(np.linalg.norm((-np.linalg.inv(D) @ (L + R)),np.inf))
+    return x
+
+
+
+A = np.array([[8,5,2],[5,9,1],[4,2,7]])
+b = np.array([[19],[5],[34]])
+x = np.array([[1],[-1],[3]])
+steps = 3
+print(Jacobi(A,b,x,steps))
+print("Sum of vector:")
+#print(np.sum(Jacobi(A,b,x,steps)))
+#print(np.linalg.norm(Jacobi(A,b,x,3)-Jacobi(A,b,x,2),np.inf)*7)
+print(np.linalg.norm(Jacobi(A,b,x,3)-Jacobi(A,b,x,2),np.inf))
+print((0.0001*0.125)/0.7693452380952384)

Schenk_Brandenberger_S10_Aufg2.py

@@ -0,0 +1,21 @@
+import numpy as np
+
+print("*********Gauss Seidel*********")
+def Gauss_Seidel(A,b,x,steps):
+    L = np.tril(A,k=-1)
+    D = np.diag(np.diag(A))
+    R = np.triu(A, k=1)
+    print(np.linalg.norm(-np.linalg.inv(D+L) @ R,np.inf))
+    for steps in range(steps):
+        x = -np.linalg.inv(D+L) @ R @ x + np.linalg.inv(D+L) @ b
+    return x
+
+
+A = np.array([[8,5,2],[5,9,1],[4,2,7]])
+b = np.array([[19],[5],[34]])
+x = np.array([[1],[-1],[3]])
+steps = 3
+print(Gauss_Seidel(A,b,x,steps))
+print("Sum of vector:")
+print(np.sum(Gauss_Seidel(A,b,x,steps)))
+print(np.linalg.norm(Gauss_Seidel(A,b,x,3)-Gauss_Seidel(A,b,x,2),np.inf))