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In the 90s, Dhillon and Parlett devised a new algorithm (Multiple Relatively Robust Representations, MRRR) for computing numerically orthogonal eigenvectors of a symmetric tridiagonal matrix T with O(n^2) cost. In this paper, we describe the design of PDSYEVR, a ScaLAPACK implementation of the MRRR algorithm to compute the eigenpairs in parallel. It represents a substantial improvement over the symmetric eigensolver PDSYEVX that is currently in ScaLAPACK and is going to be part of the next ScaLAPACK release.

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