How can I get the (approximate) eigenvectors of a huge matrix?

I have a huge symmetric matrix M and I want to get the eigenvectors to the k smallest eigenvalues of M (which have to be greater than 0). I know that the smallest eigenvalue is 0.

Currently I am using

 eigs(M,k,eps)

but this results in memory consumption of over 100GB of RAM.

[Matt J]

but this results in memory consumption of over 100GB of RAM.

It's pretty impressive that you have that much RAM! Time for me to upgrade, I guess...

[Steffen]

Actually I have 128GB but the systems also needs some resources. Nonetheless my memory is not enough. It was swapping something like 50GB so I don't know how much memory there would be needed... (Even 200GB might be not enough.)

Therefore I am open for suggestions. M is a 150k x 150k matrix. Are there any approximate methods which need much less memory?

[Matt J]

I don't really understand why it's taking so much memory. What happens when you do

eigs(M,k,'sm')

Answer 1

[Thorsten]

If M contains many 0's you can define M as a sparse matrix to speed up computation.

[Steffen]

M is already defined as sparse. I construct the matrix by using spconvert().

Answer 2

[Andrew Knyazev]

try http://www.mathworks.com/matlabcentral/fileexchange/48-lobpcg-m