The solution of the symmetric eigenproblem PDSYEVX consists of three phases: (1) reduce the original matrix to tridiagonal form where is orthogonal and is tridiagonal, (2) find the eigenvalues and eigenvectors of so that , and (3) form the eigenvector matrix of so . Phases 1 and 3 are analogous to their LAPACK counterparts, similarly to LU. However, our current design for phase 2 differs from the serial (or shared memory) design. We have chosen to do bisection followed by inverse iteration (like the LAPACK expert driver DSYEVX), but with the reorthogonalization phase of inverse iteration limited to the eigenvectors stored in a single process. A straightforward parallelization of DSYEVX would have led to a serial bottleneck and significant slowdowns in the rare situation of matrices with eigenvalues tightly clustered together. The current design guarantees that phase (2) is inexpensive compared to the other phases once problems are reasonably large. An alternative algorithm which completely eliminates the need for reorthogonalization has recently been discovered by Parlett, Fernando, and Dhillon , and we expect to use this version of the routine in the near future. This new routine will guarantee high accuracy and high speed independent of the eigenvalue distribution.