Network flows as least squares solvers for linear equations
Yang Liu, Youcheng Lou, Brian D. O. Anderson, Guodong Shi · 2017
This paper presents a first-order continuous-time distributed step-size algorithm for computing the least squares solution to a linear equation over networks. Given the uniqueness of the solution and nonintegrable step size, the convergence results are provided for fixed graphs. For the nonunique solution and square integrable step size, the convergence is shown for constantly connected switching graphs. We also validate the results and illustrate possible impacts on the convergence speed using a few numerical examples.