  In this paper, an efficient divide-and-conquer (DC) algorithm is proposed for
the symmetric tridiagonal matrices based on ScaLAPACK and the hierarchically
semiseparable (HSS) matrices. HSS is an important type of rank-structured
matrices.Most time of the DC algorithm is cost by computing the eigenvectors
via the matrix-matrix multiplications (MMM). In our parallel hybrid DC (PHDC)
algorithm, MMM is accelerated by using the HSS matrix techniques when the
intermediate matrix is large. All the HSS algorithms are done via the package
STRUMPACK. PHDC has been tested by using many different matrices. Compared with
the DC implementation in MKL, PHDC can be faster for some matrices with few
deflations when using hundreds of processes. However, the gains decrease as the
number of processes increases. The comparisons of PHDC with ELPA (the
Eigenvalue soLvers for Petascale Applications library) are similar. PHDC is
usually slower than MKL and ELPA when using 300 or more processes on Tianhe-2
supercomputer.
