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Homework 4

# Thisisoppositeoftheprogressionofmodesinthecaseofequalm

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Unformatted text preview: 33 0.666666666666667 0.633974596215561 >> [v e] = eig(B) v = ‐0.930189805014032 ‐0.577350269189626 0.403143528319302 0.360379610028063 ‐0.577350269189626 0.693712943361396 ‐0.069810194985968 0.577350269189626 0.596856471680699 e = 2.387425886722794 0 0 0 1.000000000000000 0 0 0.279240779943874 0 Here, as was seen in the first example of unequal masses, the highest mode corresponds to the first column of v, the second highest to the second column of v, and the lowest mode ties into the third column of v. This is opposite of the progression of modes in the case of equal masses. 16.1) The function, powermethod, performs the Power Method on a given symmetric matrix Anxn until the change between vectors obtained is less than a given tolerance. After the tolerance has been met, the program outputs the number of iterations to achieve the tolerance, the largest eigenvalue of A, and a vector which is equal to one of the eigenvectors of A divided by the norm of that eigenvector. As A increased in size, never did the number of iterations reach beyond 6 times the dimension of A. Otherwise, the number of iterations needed varied greatly inside of that bound. The following is the code for powermethod: function [i ev ew] = powermethod(A,tol) % % % % PowerMethod performs the Power Method on a given symmetric matrix A. A -- square matrix tol -- tolerance to determine when x has stopped changing % Obtain the column dimension of A n = size(A,1); x = ones(n,1); % Set the two vecto...
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