论文标题
部分可观测时空混沌系统的无模型预测
Convergence Rate of a Message-passing Algorithm for Solving Linear Systems
论文作者
论文摘要
本文研究了用于解决大规模线性系统的消息传递分布式算法的收敛速率。这个问题是从统计学习和分布式信号处理的著名高斯信仰传播（BP）问题中概括的，并且该消息通讯算法是从良好的高斯BP算法中概括的。在普遍的对角线占主导地位的假设下，我们通过艰苦的推导揭示了有关消息通讯算法的收敛速率的几个界限。特别是，我们清楚地展示了如何使用系统的对角线优势特性显式地界定算法的收敛速率。当专门研究高斯BP问题时，我们的工作还为BP算法的行为提供了新的理论见解，因为我们使用纯线性代数方法进行收敛分析。
This paper studies the convergence rate of a message-passing distributed algorithm for solving a large-scale linear system. This problem is generalised from the celebrated Gaussian Belief Propagation (BP) problem for statistical learning and distributed signal processing, and this message-passing algorithm is generalised from the well-celebrated Gaussian BP algorithm. Under the assumption of generalised diagonal dominance, we reveal, through painstaking derivations, several bounds on the convergence rate of the message-passing algorithm. In particular, we show clearly how the convergence rate of the algorithm can be explicitly bounded using the diagonal dominance properties of the system. When specialised to the Gaussian BP problem, our work also offers new theoretical insight into the behaviour of the BP algorithm because we use a purely linear algebraic approach for convergence analysis.
