A Parallel Eigensolver for Dense Symmetric Matrices*

We describe a parallel algorithm for finding the eigenvalues and eigenvectors of a dense symmetric matrix. We follow the traditional three step process: we reduce the dense matrix to tridiagonal form, solve the tridiagonal problem then backtransform the result. Since the different steps have different algorithmic characteristics, this problem serves as an perfect vehicle for exploring some issues associated with parallel linear algebra calculations, In particular we examine the effects of matrix distribution and blocking on the computational performance of tridiagonalization and backtransformation. Through experiments on an Intel Paragon, we demonstrate that block storage of the matrix is not necessary for a highly efficient block algorithm. We compare the performance of our implementations to that of the corresponding ScaLapack routines.