A parallel algorithm for the non-symmetric eigenvalue problem

We report on an algorithm for the solution of the non-symmetric eigenvalue problem. The algorithm is based on a divide and conquer procedure that provides initial approximations to the eigenpairs which are then refined using Newton iterations. Since the smaller subproblems can be solved independently, and since Newton iterations with different initial guesses can be started simultaneously, the algorithm -unlike the standard QR method- is ideal for parallel computers. We also report on our investigation of deflation methods designed to obtain further eigenpairs if needed. Numerical results from implementations on a host of parallel machines (distributed and shared-memory) will be given.