The decentralized solution of linear systems of equations arises as a subproblem in optimization over networks. Typical examples include the KKT system corresponding to equality constrained quadratic programs in distributed optimization algorithms or in active set methods. This note presents a tailored structure-exploiting decentralized variant of the conjugate gradient method. We show that the decentralized conjugate gradient method exhibits super-linear convergence in a finite number of steps. Finally, we illustrate the algorithm's performance in comparison to the Alternating Direction Method of Multipliers drawing upon examples from sensor fusion.

中文翻译：

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具有有限步收敛的分散共轭梯度

线性方程组的分散式解决方案是网络优化中的一个子问题。典型示例包括与分布式优化算法或活动集方法中的等式约束二次程序相对应的KKT系统。本说明介绍了共轭梯度方法的量身定制的利用结构的分散式变体。我们表明，分散共轭梯度法在有限数量的步骤中表现出超线性收敛。最后，我们以传感器融合为例，说明了与乘数交替方向法相比的算法性能。