A Distributed Eigensolver for Loosely Coupled Networks

We introduce a new distributed eigensolver (dOI) for square matrices based on orthogonal iteration. In contrast to standard parallel eigensolvers, our approach performs only nearest neighbor communication and provides much more flexibility with respect to the properties of the hardware infrastructure on which the computation is performed. This is achieved by utilizing distributed summation methods with randomized communication schedules which do not require global synchronization across the nodes. Our algorithm is particularly attractive for loosely coupled distributed networks with arbitrary network topologies and potentially unreliable components. Our distributed eigensolver dOI is based on a novel distributed matrix-matrix multiplication algorithm and on an extension of a distributed QR factorization algorithm proposed earlier. We illustrate the advantages of dOI in terms of higher flexibility with respect to the underlying network and lower communication cost compared to a related distributed eigensolver by Kempe and McSherry. Moreover, we experimentally illustrate how the overall communication cost of dOI is further reduced by adapting the accuracy of each distributed summation during the orthogonal iteration process.