The Shifted Inverse Power Method Suppose that u is not an eigenvalue of A (a) Show that the iterative scheme u(k 1) (A I) 1 u(k) converges to the eigenvector of A corresponding to the eigenvalue that is closest to Explain how to find the eigenvalue (b) What is the rate of convergence of the algorithm (c) What happens if is an eigenvalue

Question: The Shifted Inverse Power Method. Suppose that u is not an eigenvalue of A. (a) Show that the iterative scheme u(k+1) = (A -

The Shifted Inverse Power Method. Suppose that u is not an eigenvalue of A.
(a) Show that the iterative scheme u(k+1) = (A - μ I)-1 u(k) converges to the eigenvector of A corresponding to the eigenvalue λ* that is closest to μ. Explain how to find the eigenvalue λ*.
(b) What is the rate of convergence of the algorithm?
(c) What happens if μ is an eigenvalue?

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