  Graph analytics techniques based on spectral methods process extremely large
sparse matrices with millions or even billions of non-zero values. Behind these
algorithms lies the Top-K sparse eigenproblem, the computation of the largest
eigenvalues and their associated eigenvectors. In this work, we leverage GPUs
to scale the Top-K sparse eigenproblem to bigger matrices than previously
achieved while also providing state-of-the-art execution times. We can
transparently partition the computation across multiple GPUs, process
out-of-core matrices, and tune precision and execution time using
mixed-precision floating-point arithmetic. Overall, we are 67 times faster than
the highly optimized ARPACK library running on a 104-thread CPU and 1.9 times
than a recent FPGA hardware design. We also determine how mixed-precision
floating-point arithmetic improves execution time by 50% over double-precision,
and is 12 times more accurate than single-precision floating-point arithmetic.

Hardware Architecture