AN ALGORITHM AND PROGRAM OF SOLVING

THE PROBLEM OF EIGEN VALUES

AN ITERATION METHOD

One of the solutions could be using Moore-Penrose pseudoinverse of matrix. This can be obtained using pinv function in Matlab.

I tried with the matrices provided by you and it seems to work and did not result in inf eigenvalue. You can use the following code:

load('M11.mat');load('M12.mat');load('M21.mat');load('M22.mat');

load('K11.mat');load('K12.mat');load('K21.mat');load('K22.mat');

K = [K11 K12; K21 K22];

M = [M11 M12; M21 M22];

[v d] = eig(pinv(M)*K);

diag(d)

Still I would suggest you to have a closer look into the eigenvalues to ensure the correctness of the solution.

Hope this helps.

Looks like the equations of a mechanical system with N linear constraints. If this is true compute a QR decomposition of the constraint matrix K12. Use Q(:,N+1:M) to project K11 and M11 onto the free modes and solve the reduced general eigenvalue problem for the projected system. Some details are in the attached pdf.