## Distributed Solution of Large-Scale Linear Systems via Accelerated Projection-Based Consensus. (arXiv:1708.01413v1 [cs.LG])

Solving a large-scale system of linear equations is a key step at the heart
of many algorithms in machine learning, scientific computing, and beyond. When
the problem dimension is large, computational and/or memory constraints make it
desirable, or even necessary, to perform the task in a distributed fashion. In
this paper, we consider a common scenario in which a taskmaster intends to
solve a large-scale system of linear equations by distributing subsets of the
equations among a number of computing machines/cores. We propose an accelerated
distributed consensus algorithm, in which at each iteration every machine
updates its solution by adding a scaled version of the projection of an error
signal onto the nullspace of its system of equations, and where the taskmaster
conducts an averaging over the solutions with momentum. The convergence
behavior of the proposed algorithm is analyzed in detail and analytically shown
to compare favorably with the convergence rate of alternative distribu查看全文