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Reverse power method

anurag3301 answered on June 26, 2023 Popularity 1/10 Helpfulness 1/10

answer Reverse power method

Reverse power method

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import numpy as np

def reverse_power_method(A, max_iterations=1000, tolerance=1e-6):
    # Compute the inverse of A
    A_inv = np.linalg.inv(A)

    # Initialize a random vector
    n = A.shape[0]
    x = np.random.rand(n)
    x /= np.linalg.norm(x)

    # Perform reverse power iteration
    for i in range(max_iterations):
        # Apply matrix multiplication
        y = np.dot(A_inv, x)

        # Compute the eigenvalue estimate
        eigenvalue = np.dot(x, y)

        # Normalize the eigenvector estimate
        x_new = y / np.linalg.norm(y)

        # Check convergence
        if np.linalg.norm(x - x_new) < tolerance:
            break

        x = x_new

    # Compute the corresponding eigenvector
    eigenvector = x_new

    # Compute the actual eigenvalue by taking its reciprocal
    eigenvalue = 1 / eigenvalue

    return eigenvalue, eigenvector

Popularity 1/10 Helpfulness 1/10 Language python

Source: chat.openai.com

Tags: python reverse

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Contributed on Jun 26 2023

anurag3301

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