Distributed computation in numerical linear algebra

Large-scale numerical linear algebra algorithms have been fundamental in computation, since the early days of the computing. Driven by a change in hardware architecture, emerging topics in linear algebra not only consider the number of operations to be carried out, but how well the algorithm can be executed in parallel. Limitations of traditional algorithms on modern architectures can often be traced back to the transfer of data and communication between processing units, both in a shared memory, as well as distributed memory setting.

To meet the need to analyze an increasing amount of data, new algorithms in the area take the transfer of data into account. Breakthroughs that have enabled large-scale distributed numerical linear algebra include Cauchy integral formulations, Hierarchical matrix representation formats and randomization. In this talk we review some of these development in low-communication algorithms for distributed computing.