The Shifted Inverse Power Method. Suppose that u is not an eigenvalue of A. (a) Show that
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(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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