Use the power method, in Matlab to determine the highest eigenvalue and correspo

Question

Use the power method, in Matlab to determine the highest eigenvalue and corresponding eigenvector for the matrix

Use the power method to determine the highest eigenvalue and corresponding eigenvector for the matrix Show four iterations of your hand calculations, starting with an initial guess for the eigenvector {111}T. Also, use the powereig.m M-file function discussed in class (posted on Canvas under Lecture 16) to obtain the eigenvalue within 0.01% accuracy using MATLAB.

Explanation / Answer

function l = ww(A,E) n = length(A); y = []; x = []; for i = 1:n % starting vector x(i) = A(i,1); end; l = 0; blad = E; % starting value of error while blad>=E for i = 1:n % A*x y(i) = 0; for j = 1:n y(i) = y(i) + A(i,j)*x(j); end; end; blad = l; l = 0; % Rayleigh m = 0; for i = 1:n l = l + x(i)*y(i); m = m + x(i)*x(i); end; l = l/m; % eigenvalue blad = abs(l - blad); % error x = y; end; end

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