A performance analysis of parallel eigensolvers for large dense symmetric matrices

The correct determination of eigenvalues of a matrix is extremely important in various computational sciences disciplines such as quantum physics, quantum chemistry statistics orengineering. Finding eigenvalues corresponds to diagonalizing a matrix, a joint operation in various applications such as solving algebraic equations, stability theory, and the analysis of small oscillations in a vibrating system etc. Eigensolvers prove to be useful in building simulators of various processes. However, in simulation, for obtaining results with a high accuracy it is necessary to model a huge number of events that involve large-scale computational resources and significant amounts of time. In this case, the parallelization of simulation represents a demand and the solution employs high performance parallel processing algorithms. The goals of this paper are to develop a ScaLAPACK-based experimental environment and to analyze the performance of this parallel solution to compute the eigenvalues and eigenvectors of a matrix considering the architecture features of IBM Roadrunner cluster and HPCx systems. The results of performance comparison study of two parallel eigensolvers provided by ScaLAPACK library demonstrate a strong scaling capability of IBM Roadrunner cluster for problems which imply large dense algebra operations in contrast with those large parallel machines such as HPCx.