Apply the power method to find the highest eigenvalue for the inverse of Matrix A = [2 -3 1; -2 5 -2; 3 -2 -5] in Matlab. Set the stopping criterion as 1% (Estimated Eigenvector need to be normalized). Estimated Eigenvector (normalized) and Estimated High
时间: 2024-02-18 15:59:59 浏览: 21
Sure, I can help you with that. Here's how you can apply the power method to find the highest eigenvalue for the inverse of Matrix A in Matlab:
```matlab
% Define the matrix A
A = [2 -3 1; -2 5 -2; 3 -2 -5];
% Set the stopping criterion as 1%
tolerance = 0.01;
% Initialize the estimated eigenvector
x = [1; 1; 1];
% Iterate until convergence
while true
% Calculate the next estimate of the eigenvector
x_new = inv(A) * x;
% Normalize the estimate
x_new = x_new / norm(x_new);
% Calculate the corresponding eigenvalue
lambda = x_new' * inv(A) * x_new;
% Check for convergence
if norm(x_new - x) < tolerance
break;
end
% Update the estimate
x = x_new;
end
% Display the results
fprintf('Estimated Eigenvector: \n');
disp(x_new);
fprintf('Estimated Highest Eigenvalue: %.4f \n', lambda);
```
This code should output the estimated eigenvector and the estimated highest eigenvalue for the inverse of Matrix A.