I tried dgedd routines from https://software.intel.com/en-us/node/521149
My matrix is 100K by 30K, about 24 GB in size. I am using MKL 11.3 on a windows server with about 300 GB memory. The routines failed with error message "Not enough memory to allocate work array".
On my desktop with 32 GB memory I am able to perform SVD of 100K by 13K matrix. In my case work array size should scales quadratically with number of colomns, so going from 13K to 30K should be possible.