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In this paper, an efficient divide-and-conquer (DC) algorithm is proposed forthe symmetric tridiagonal matrices based on ScaLAPACK and the hierarchicallysemiseparable (HSS) matrices. HSS is an important type of rank-structuredmatrices.Most time of the DC algorithm is cost by computing the eigenvectorsvia the matrix-matrix multiplications (MMM). In our parallel hybrid DC (PHDC)algorithm, MMM is accelerated by using the HSS matrix techniques when theintermediate matrix is large. All the HSS algorithms are done via the packageSTRUMPACK. PHDC has been tested by using many different matrices. Compared withthe DC implementation in MKL, PHDC can be faster for some matrices with fewdeflations when using hundreds of processes. However, the gains decrease as thenumber of processes increases. The comparisons of PHDC with ELPA (theEigenvalue soLvers for Petascale Applications library) are similar. PHDC isusually slower than MKL and ELPA when using 300 or more processes on Tianhe-2supercomputer.

An efficient hybrid tridiagonal divide-and-conquer algorithm on distributed memory architectures