The Performance of Finding Eigenvalues and Eigenvectors of Dense Symmetric Matrices on Distributed Memory Computers

We discuss timing and performance modeling of a routine to find all the eigenvalues and eigenvectors of a dense symmetric matrix on distributed memory computers. The routine, PDSYEVX, is part of the ScaLAPACK library. It is based on bisection and inverse iteration, but is not designed to guarantee orthogonality of eigenvectors in the presence of clustered eigenvalues. We use our validated performance model to conclude that PDSYEVX is very efficient for large enough problem sizes, nearly independently of input and output data layouts. However, efficiency will be low if interprocessor communication is too slow, such as on conventional workstation networks, or if per processor memory is too small, such as on the Intel Gamma. Modeling also helps us choose the appropriate algorithm to deal with clusters. 1 Summary There are many algorithms for solving the dense symmetric eigenproblem[11]. Most of them consist of 3 steps: 1) reduce the dense matrix to tridiagonal form, 2) find the eigenvalu..