  Since the initial proposal in the late 80s, spectral gradient methods
continue to receive significant attention, especially due to their excellent
numerical performance on various large scale applications. However, to date,
they have not been sufficiently explored in the context of distributed
optimization. In this paper, we consider unconstrained distributed optimization
problems where $n$ nodes constitute an arbitrary connected network and
collaboratively minimize the sum of their local convex cost functions. In this
setting, building from existing exact distributed gradient methods, we propose
a novel exact distributed gradient method wherein nodes' step-sizes are
designed according to the novel rules akin to those in spectral gradient
methods. We refer to the proposed method as Distributed Spectral Gradient
method (DSG).
  The method exhibits R-linear convergence under standard assumptions for the
nodes' local costs and safeguarding on the algorithm step-sizes. We illustrate
the method's performance through simulation examples.
