广播八卦平均算法的渐近误差
The asymptotical error of broadcast gossip averaging algorithms
AI总结：
针对网络平均值的分布式计算问题，利用鞅理论证明了广播八卦迭代算法中累积误差的期望上界仅依赖于混合参数、网络规模、最大度数和谱隙，并表明在多种应用网络拓扑中误差随网络规模增大而趋于零。
摘要：
在涉及网络的估计与控制问题中，高效的分布式平均值计算是一个关键问题。本文通过迭代“广播八卦”算法计算平均值时误差累积的理论和仿真结果。利用鞅理论，我们证明累积误差的期望可以由一个仅依赖于算法的混合参数以及网络的少数性质（规模、最大度数和谱隙）的量从上方界定。分析结果和计算机仿真均表明，在若干具有应用兴趣的网络拓扑中，累积误差随着网络规模的增大而趋于零。
英文摘要：
In problems of estimation and control which involve a network, efficient distributed computation of averages is a key issue. This paper presents theoretical and simulation results about the accumulation of errors during the computation of averages by means of iterative "broadcast gossip" algorithms. Using martingale theory, we prove that the expectation of the accumulated error can be bounded from above by a quantity which only depends on the mixing parameter of the algorithm and on few properties of the network: its size, its maximum degree and its spectral gap. Both analytical results and computer simulations show that in several network topologies of applicative interest the accumulated error goes to zero as the size of the network grows large.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
