Parallel subspace iteration method for the sparse symmetric eigenvalue problem

A new parallel iterative algorithm for the diagonalization of real sparse symmetric matrices is introduced, which uses a modified subspace iteration method. A novel feature is the preprocessing of the matrix prior to iteration, which allows for a natural parallelization resulting in a great speedup and scalability of the method with respect to the number of compute nodes. The method is applied to Hamiltonian matrices of model systems up to six degrees of freedom, represented in a truncated Weyl-Heisenberg wavelet (or "weylet") basis developed by one of the authors (Poirier). It is shown to accurately determine many thousands of eigenvalues for sparse matrices of the order N ≈ 10⁶, though much larger matrices may also be considered.