Title: Network Flows that Solve Least Squares for Linear Equations,
Abstract: This paper presents a first-order {distributed continuous-time algorithm} for
computing the least-squares solution to a linear equation over networks. Given
the uniqueness of the solution, with nonintegrable and diminishing step size,
convergence results are provided for fixed graphs. The exact rate of
convergence is also established for various types of step size choices falling
into that category. For the case where non-unique solutions exist, convergence
to one such solution is proved for constantly connected switching graphs with
square integrable step size, and for uniformly jointly connected switching
graphs under the boundedness assumption on system states. Validation of the
results and illustration of the impact of step size on the convergence speed
are made using a few numerical examples.