A fast algorithm for the symmetric eigenvalue problem

The symmetric eigenvalue problem is one of the most fundamental problems of computational mathematics. It arises in many applications, and therefore represents an important area for algorithmic research. It is also one of the first eigenvalue problems for which reliable methods have been obtained. It would be surprising therefore, if a new method were to be found that would offer a significant improvement in execution time over the fundamental algorithms available in standard software packages such as EISPACK [7]. However, it is reasonable to expect that eigenvalue calculations might be accelerated through the use of parallel algorithms for parallel computers that are emerging. We shall present such an algorithm in this paper. The algorithm is able to exploit parallelism at all levels of the computation and is well suited to a variety of architectures. However, a pleasant bonus of this research is that the parallel algorithm, even when run in serial mode, is significantly faster than the best sequential algorithm on large problems, and is effective on moderate size (order ≥30) problems when run in serial mode.