Serie 10

Kuengjoe_S10/Kuengjoe_S10_Aufg1_python.py

@@ -0,0 +1,35 @@
+import numpy as np
+
+A = np.array([[8, 5, 2],
+              [5, 9, 1],
+              [4, 2, 7]], dtype=float)
+
+b = np.array([19, 5, 34], dtype=float)
+x_start = np.array([1, -1, 3], dtype=float)
+x_exact = np.array([2, -1, 4], dtype=float)
+
+D = np.diag(np.diag(A))
+L_plus_U = A - D
+inv_D = np.linalg.inv(D)
+
+
+B_jacobi = -np.dot(inv_D, L_plus_U)
+alpha = np.linalg.norm(B_jacobi, np.inf)
+#german text
+print(f"Alpha (Faktor von Kontraktion): {alpha}")
+
+
+x_curr = x_start.copy()
+print(f"x(0) = {x_curr}")
+
+x_history = [x_curr.copy()]
+
+for k in range(1, 4):
+    x_new = np.dot(inv_D, (b - np.dot(L_plus_U, x_curr)))
+
+    print(f"x({k}) = {x_new}")
+    x_history.append(x_new)
+    x_curr = x_new
+
+print("-" * 30)
+print(f"Näherungslösung x(3): {np.around(x_curr, 4)}")

Kuengjoe_S10/Kuengjoe_S10_Aufg2_python.py

@@ -0,0 +1,25 @@
+import numpy as np
+
+A = np.array([[8, 5, 2], [5, 9, 1], [4, 2, 7]], dtype=float)
+b = np.array([19, 5, 34], dtype=float)
+x_k = np.array([1, -1, 3], dtype=float)
+U = np.triu(A, 1)
+DL = np.tril(A)
+
+DL_inv = np.linalg.inv(DL)
+
+print(f"Startvektor x(0): {np.around(x_k, 4)}")
+x_history = [x_k.copy()]
+
+for k in range(1, 4):
+    x_new = np.dot(DL_inv, (b - np.dot(U, x_k)))
+    x_history.append(x_new.copy())
+    x_k = x_new
+    print(f"x({k}): {np.around(x_k, 4)}")
+
+x_1 = np.array([2.7500, -1.4167, 3.5714])
+x_2 = np.array([2.1190, -1.0873, 3.9780])
+x_3 = np.array([1.9861, -0.9945, 4.0049])
+
+print("-" * 35)
+print(f"Näherung x(3) (4 Dezimalstellen): {x_3}")