How can I estimate how much memory will be needed to find eigenvalues and eigenvectors of a given large sparse matrix?
I have a real symmetric matrix with roughly $5 \times 10^4$ rows and columns, and an average of $10$ nonzero elements per row. I would like to find the smallest eigenvalue and the corresponding eigenvector, using the built-in
Eigensystem function in Mathematica (which treats the matrix as sparse and uses an ARPACK Arnoldi algorithm). Is there a simple way of estimating how much memory this will take?