自稳定数值迭代计算
Self-stabilizing Numerical Iterative Computation
AI总结：
提出一种自稳定迭代算法SS-Iterative用于求解线性方程组，在输入变化时仍能收敛，并应用于传感器校准问题。
摘要：
传感器网络中的许多挑战性任务，包括传感器校准、节点排名、监控、事件区域检测、协同过滤、协同信号处理等，都可以归结为求解线性方程组的问题。最近的一些工作提出了不同的分布式算法来解决这些问题，通常使用线性迭代数值方法。先前方法的主要问题是，一旦计算过程中问题输入发生变化，计算可能会输出意外结果。在现实环境中，传感器测量受到变化的环境条件和测量噪声的影响。我们提出了一种简单的迭代方案，称为SS-Iterative，用于求解线性方程组，并从自稳定的角度研究其性质。我们使用两种不同的输入假设（箱形边界和概率分布）分析了所提方案在输入序列变化下的行为。作为案例研究，我们讨论了传感器校准问题，并提供了仿真结果以支持我们方法的适用性。
英文摘要：
Many challenging tasks in sensor networks, including sensor calibration, ranking of nodes, monitoring, event region detection, collaborative filtering, collaborative signal processing, {\em etc.}, can be formulated as a problem of solving a linear system of equations. Several recent works propose different distributed algorithms for solving these problems, usually by using linear iterative numerical methods. The main problem with previous approaches is that once the problem inputs change during the process of computation, the computation may output unexpected results. In real life settings, sensor measurements are subject to varying environmental conditions and to measurement noise. We present a simple iterative scheme called SS-Iterative for solving systems of linear equations, and examine its properties in the self-stabilizing perspective. We analyze the behavior of the proposed scheme under changing input sequences using two different assumptions on the input: a box bound, and a probabilistic distribution. As a case study, we discuss the sensor calibration problem and provide simulation results to support the applicability of our approach.
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