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Eigenvalue Numerical Computation
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Module 1
The Power Method and its Variants
1
The Power Method: Iteration and Convergence
Explain the iterative principle of the Power Method and its convergence conditions.
2
The Power Method for Eigenvalues and Eigenvectors
Apply the Power Method to compute the dominant eigenvalue and corresponding eigenvector of a matrix.
3
Inverse Power Method for Smallest Eigenvalue
Use the Inverse Power Method to find the eigenvalue of a matrix with the smallest magnitude.
4
Shifted Inverse Power Method for Closest Eigenvalue
Use the Shifted Inverse Power Method to find the eigenvalue of a matrix closest to a given scalar.
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Reduction to Tridiagonal Form