How does "svds" function find singular values ?

I've come across a paper where it says that svds uses ARPACK library routines to compute the singular values. If I am not wrong ARPACK uses implicitly restarted Lanczos Bidiagonalisation method for finding eigenvalues which in turn can be used to find singular values from the augmented matrix C

I was trying to get smallest singular value of A of size 1.5x10^6 x 1.5x10^6 (sparse with nnz=7.5x10^6(approx)). It was showing out of memory. Does this algorithm or function "svds" have any memory constraints ?