to develop a MATLAB program for eigenvalue solving using MATRIX ITERATION method

Question

Muhammad 2022-12-6

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1872192-to-develop-a-matlab-program-for-eigenvalue-solving-using-matrix-iteration-method

回答： Vinay 2024-8-8，9:16

I am trying to create a program which will compute eigenvalue using matrix iteration method. I just know some basic commands and still learning. I have created the following function but I know it has a lot of errors and is not complete. Can anyone plz help

function l = ww(m,k)

for i=1:1000

for j=1:1000

m = [i 0 0;0 2*i 0;0 0 i];

k = [2*j -j 0;-j 7*j -4*j;0 -4*j 5*j];

end

n = length(m);

y = [];

x = [];

for i = 1:n % starting vector

x(i) = m(i,1);

end;

l = 0;

blad = k; % starting value of error

while blad>=k

for i = 1:n % A*x

y(i) = 0;

for j = 1:n

y(i) = y(i) + m(i,j)*x(j);

end;

blad = l;

l = 0; % Rayleigh

t = 0;

for i = 1:n

l = l + x(i)*y(i);

t = t + t(i)*x(i);

end;

l = l/t; % eigenvalue

blad = abs(l - blad); % error

x = y;

end;

end

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Vinay 2024-8-8，9:16

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1872192-to-develop-a-matlab-program-for-eigenvalue-solving-using-matrix-iteration-method#answer_1496549

在 MATLAB Online 中打开

Hello Muhammad

Matrix iteration method calculates the eigen vector of a square matrix by starting with an initial guess for the eigen vector, repeatedly multiplying it by the matrix, and normalizing the result until convergence is achieved.

MATLAB function “rand” can be used for generating initial eigen vector and “norm” function for normalizing the eigen vector.

Kindly refer to the following documentations for “rand” and “norm” functions:

function [eigenvalue, eigenvector] = power_iteration(A, tol, max_iter)
    % A: Square matrix
    % tol: Tolerance 
    % max_iter: Maximum number of iterations
    [~,n] = size(A);
    % Initial guess for the eigenvector
    b_k = rand(n, 1);
    % Normalize the initial vector
    b_k = b_k / norm(b_k);
    % Iteration
    for k = 1:max_iter
        % Multiply by matrix A
        b_k1 = A * b_k;
        % Normalize the eigen vector
        b_k1 = b_k1 / norm(b_k1);
        % Check whether convergence is achieved 
        if norm(b_k1 - b_k) < tol
            break;
        end
        % Update the eigen vector
        b_k = b_k1;
    end
    % The dominant eigenvalue
    eigenvalue = b_k' * A * b_k;
    % The corresponding eigenvector
    eigenvector = b_k;
end
% Example
A = [4, 1; 5, 3];
tol = 1e-6;
max_iter = 1000;
[eigenvalue, eigenvector] = power_iteration(A, tol, max_iter);
disp(['Dominant Eigenvalue: ', num2str(lambda)]);
disp('Corresponding Eigenvector:');
disp(eigenvector);