  Solving structured systems of linear equations in a non-centralized fashion
is an important step in many distributed optimization and control algorithms.
Fast convergence is required in manifold applications. Known decentralized
algorithms, however, typically exhibit asymptotic convergence at a linear rate.
This note proposes an essentially decentralized variant of the Conjugate
Gradient algorithm (d-CG). The proposed method exhibits a practical superlinear
convergence rate and comes with a priori computable finite-step convergence
guarantees. In contrast to previous works, we consider sum-wise decomposition
instead of row-wise decomposition which enables application in multi-agent
settings. We illustrate the performance of d-CG on problems from sensor fusion
and compare the results to the widely-used Alternating Direction Method of
Multipliers.
