Systematic Review of Newton-Schulz Iterations with Unified Factorizations : Integration in the Richardson Method and Application to Robust Failure Detection in Electrical Networks

TL;DR

This paper provides a comprehensive review of Newton-Schulz and Durand iterations, integrating them into the Richardson method, and applies this to robust failure detection in electrical networks, demonstrating improved performance over standard methods.

Contribution

It introduces a unified framework for Newton-Schulz and Durand iterations, offers practical guidelines for their implementation, and applies the integrated approach to electrical failure detection with robustness enhancements.

Findings

Effective failure detection on real electrical network data.

Robust preconditioning improves detection in rank deficient matrices.

Outperforms standard LU decomposition in simulations.

Abstract

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.