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.
Solution
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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Use the power method- in Matlab to determine the highest eigenvalue an.docx
1. 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.
Solution
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
![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.
Solution
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](https://image.slidesharecdn.com/usethepowermethod-inmatlabtodeterminethehighesteigenvaluean-230204014209-395b46d2/85/Use-the-power-method-in-Matlab-to-determine-the-highest-eigenvalue-an-docx-1-320.jpg)
