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