论文标题
牛顿 - 舒尔茨迭代的系统审查具有统一因素化：Richardson方法中的集成以及在电网络中稳健失败检测的应用
Systematic Review of Newton-Schulz Iterations with Unified Factorizations : Integration in the Richardson Method and Application to Robust Failure Detection in Electrical Networks
论文作者
论文摘要
在统一框架中，按时间顺序列出了牛顿 - 舒尔茨和杜兰迭代的系统概述。为选择算法的顺序和因素化以及将其集成到Richardson迭代中的实用建议。通过评估电气网络中信号的频率含量，将牛顿 - 舒尔茨和理查森迭代的最简单组合应用于与故障检测相关的参数估计问题。检测是对模拟软件故障的实际数据执行的，从而导致等级不足的信息矩阵。提出了对等级缺陷矩阵的强大预处理，并通过与标准LU分解方法进行比较来证明该方法的效率。
Systematic overview of Newton-Schulz and Durand iterations with convergence analysis and factorizations is presented in the chronological sequence in unified framework. Practical recommendations for the choice of the order and factorizations of the algorithms and integration into Richardson iteration are given. The simplest combination of Newton-Schulz and Richardson iteration is applied to the parameter estimation problem associated with the failure detection via evaluation of the frequency content of the signals in electrical network. The detection is performed on real data for which the software failure was simulated, which resulted in the rank deficient information matrix. Robust preconditioning for rank deficient matrices is proposed and the efficiency of the approach is demonstrated by simulations via comparison with standard LU decomposition method.
