Exercise 5.3.18 Let A-1 92 0 -1 2 (a) Using MATLAB, apply inverse iteration to A
ID: 3282035 • Letter: E
Question
Exercise 5.3.18 Let A-1 92 0 -1 2 (a) Using MATLAB, apply inverse iteration to A with shift p 9, starting with 90 1 1 1]. For simplicity, ust form B (A -9)-1 (B inv (A-9 eye (3)) in MATLAB) and iterate with B. Some of the com- mands shown in Exercise 5.3.10 may be useful here. Use format long to nore digits of your ite (b) Use [v,D] -eig (A) to get the true dominant eigenvector. Calculate the errors lla -vl2 and ratios +1-vll2/ll -vll2 for j-1, 2, 3, Compute the theoretical convergence rate (from the known eigenvalues) and compare it with these ratios. Notice that we have faster convergence than we had when we applied the power method to this same matrix in Exercise 5.3.10.Explanation / Answer
lambda = eig(A)
lambda = eig(A, balanceOption)
lambda = eig(A,B)
lambda = eig(A,B,algorithm)
[V,D] = eig (_ _ _)
[V,D,W] = eig (_ _ _)
[_ _ _] = eig (_ _ _, eigvalOption)