Efficient Iterative Method for Solving the General Restricted Linear Equation

Liu, Xiaoji; Du, Weirong; Yu, Yaoming; Qin, Yonghui

doi:10.4236/jamp.2018.62039

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2022

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Cited by 2 publications

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“…The error models ( 14), (15) are valid for the algorithm (13). Higher order Durand iterations are discussed in [8], [25].…”

Section: Durand Iterationsmentioning

confidence: 99%

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

Stotsky¹

2022

Preprint

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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.

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“…The error models ( 14), (15) are valid for the algorithm (13). Higher order Durand iterations are discussed in [8], [25].…”

Section: Durand Iterationsmentioning

confidence: 99%

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

Stotsky¹

2022

Preprint

View full text Add to dashboard Cite

show abstract

Reducibility for a Class of Two-Dimensional almost Periodic System with Small Perturbation

Fan-hui¹,

Qiu²

2021

APM

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Efficient Iterative Method for Solving the General Restricted Linear Equation

Abstract: An iterative method is developed for solving the solution of the general restricted linear equation. The convergence, stability, and error estimate are given. Numerical experiments are presented to demonstrate the efficiency and accuracy.

Cited by 2 publications

References 13 publications

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

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

Reducibility for a Class of Two-Dimensional almost Periodic System with Small Perturbation

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