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?