Exercise 5.3.18 Let A= . (a) Using MATLAB, apply inverse iteration to A with shi

Question

Exercise 5.3.18 Let A= . (a) Using MATLAB, apply inverse iteration to A with shift p = 9, starting with q0 = [ 1 1 1 ]T. For simplicity, just form B = (A-9I)-1 (B = inv (A-9* eye (3)) in MATLAB) and iterate with B. Some of the commands shown in Exercise 5.3.10 may be useful here. Use format long to view more digits of your iterates. Do at least ten iterations. (b) Use [V, D] = eig(A) to get the true dominant eigenvector. Calculate the errors || qj - v||2 and ratios ||qj+1-V||2/ ||qj-V||2 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)

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