A Parallel Implementation of the Invariant Subspace Decomposition Algorithm for Dense Symmetric Matrices

We give an overview of the Invariant Subspace Decomposition Algorithm for dense symmetric matrices (SYISDA) by rst describing the algorithm, followed by a discussion of a parallel implementation of SYISDA on the Intel Delta. Our implementation utilizes an optimized parallel matrix multiplication implementation we have developed. Load balancing in the costly early stages of the algorithm is accomplished without redistribution of data between stages through the use of the block scattered decomposition. Computation of the invariant subspaces at each stage is done using a new tridiagonalization scheme due to Bischof and Sun.