Hi All,Question in short :I need to find the first k smallest eigenvalues and their corresponding eigenvectors of the large sparse real symmetric matrix. The required eigenvalues(first k smallest eigenvalues) will mostly be repeated. How do I go about my problem..?Detailed Question :I need to find the first k smallest eigenvalues and their corresponding eigenvectors of a large sparse real symmetric matrix. I found that lanczos method, sturm sequence property, bisection method and inverse iteration will solve my problem. I see that Lanczos method has computational advantages in such cases. If the required eigenvalues (k smallest eigenvalues) are not repeated Lanczos method is working good. When the required eigenvalues are repeated then it is not working properly. It finds the repeated eigenvalue only once. How do I go about my problem..?Thanks in Advance,Regards,M.Kiran Kumar.

Do you have access to MATLAB? The "eigs" function might help. You can also view the code to this function.

In R, the function is "eigen".

You can try ARPACK, it's a good package: http://www.caam.rice.edu/software/ARPAC ... l"Multiple eigenvalues offer no theoretical difficulty. This is possible through deflation techniques similar to those used with the implicitly shifted QR algorithm for dense problems. With the current deflation rules, a fairly tight convergence tolerance and sufficiently large subspace will be required to capture all multiple instances. However, since a block method is not used, there is no need to ``guess" the correct block size that would be needed to capture multiple eigenvalues."