A Parallel Implementation of the Nonsymmetric QR Algorithm for Distributed Memory Architectures

One approach to solving the nonsymmetric eigenvalue problem in parallel is to parallelize the QR algorithm. Not long ago, this was widely considered to be a hopeless task. Recent e orts have made signi cant advances, although the methods proposed up to now have su ered from scalability problems. This paper discusses an approach to parallelizing the QR algorithm that greatly improves scalability. A theoretical analysis indicates that the algorithm is ultimately not scalable, but the nonscalability does not become evident until the matrix dimension is enormous. Experiments on the Intel ParagonTM system, the IBM SP2 supercomputer, and the Intel ASCI Option Red Supercomputer are reported.