LAPACK DSYEVR is the fastest driver (except for a few cases) for symmetric eigenproblems as described here http://www.netlib.org/lapack/lug/node30.html
I. DHILLON, A new O(n2) algorithm for the symmetric tridiagonal eigenvalue/eigenvector problem, Computer Science Division Technical Report no. UCB/CSD-97-971, University of California, Berkeley, CA, May 1997.
Eigen 3.1.1 uses a symmetric QR algorithm may be similar to LAPACK DSYEV/DSYEVX.
For reference only.