Before revision:  Thanks to the high parallelism of these basic linear algebra operations, we obtain excellent performance on multi-core processors and GPUs, with large speed-ups over standard methods (up to \sim50x with respect to LAPACK and ARPACK , with respect to Davidson). When off-diagonal elements are comparable to eigengaps, IPT diverges like the quadratic map outside the Mandelbrot set; for such general matrices IPT can nevertheless be used to refine low-precision eigenvectors obtained by other methods.
After revision:  Thanks to the high parallelism of these basic linear algebra operations, we obtain excellent performance on multi-core processors and GPUs, with large speed-ups over standard methods (up to \sim50x with respect to LAPACK and ARPACK , ). For matrices which are not close to being diagonal but have well-separated eigenvalues, IPT can be be used to refine low-precision eigenvectors obtained by other methods.