Recursive versus nonrecursive Richardson algorithms: systematic overview, unified frameworks and application to electric grid power quality monitoring

Stotsky, Alexander

doi:10.1080/00051144.2022.2039989

Cited by 4 publications

(6 citation statements)

References 19 publications

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“…The error model ( 21) is obtained via explicit evaluation of (22). The algorithm ( 16) -( 21) has two independent and equally complex computational parts: the first part is associated with calculations of Γ k , L k and Γ n k , where [33].…”

Section: Convergence Rate Improvement Via Combination Of High Order N...mentioning

confidence: 99%

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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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Section: Convergence Rate Improvement Via Combination Of High Order N...mentioning

confidence: 99%

“…It is assumed that the voltage signals can be described by the model (32) with harmonic regressor (33) and fundamental frequency of 60 Hertz with four higher harmonics and unknown parameter vector ϑ. The model of the signals is given by (34) with the vector of the parameters θ * k which estimates unknown vector ϑ.…”

Section: Fault Detection On Real Datamentioning

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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“…The Nonrecursive Richardson algorithm described, for example, in [6] and [14], which requires matrix-vector multiplications, can be used directly for the calculation of the parameters 𝜃 𝑘 in ( 1)…”

Section: Nonrecursive Richardson Algorithmmentioning

confidence: 99%

“…The spectral radius of the matrix (𝐼 − 𝛼𝐴 𝑘 ) gets its minimal value (1 − 𝜆 ̂𝑚𝑖𝑛 (𝐴 𝑘 )𝛼) for the SPD matrix 𝐴 𝑘 for the preconditioner (14), where 𝜆 ̂𝑚𝑖𝑛 (𝐴 𝑘 ) and 𝜆 ̂𝑚𝑎𝑥 (𝐴 𝑘 ) are the estimates of minimal and maximal eigenvalues of 𝐴 𝑘 , respectively. In other words, the preconditioner ( 14) maps the interval containing all eigenvalues of 𝐴 𝑘 onto symmetric interval around the origin [15].…”

Section: Preconditioning Based On the Properties Of The Windowmentioning

confidence: 99%

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Recursive Estimation in the Moving Window: Efficient Detection of the Distortions in the Grids with Desired Accuracy

Stotsky

2022

J. Adv. App. Comput. Math.

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The development of fast convergent and computationally efficient algorithms for monitoring waveform distortions and harmonic emissions will be an important problem in future electrical networks due to the high penetration level of renewable energy systems, smart loads, new types of power electronics, and many others. Estimating the signal quantities in the moving window is the most accurate way of monitoring these distortions. Such estimation is usually associated with significant computational loads, which can be reduced by utilizing the recursion and information matrix properties. Rank two update representation of the information matrix allows the derivation of a new computationally efficient recursive form of the inverse of this matrix and recursive parameter update law. Newton-Schulz and Richardson correction algorithms are introduced in this paper to prevent error propagation and for accuracy maintenance. Extensive comparative analysis is performed on real data for proposed recursive algorithms and the Richardson algorithm with an optimally chosen preconditioner. Recursive algorithms show the best results in estimation with ill-conditioned information matrices.

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Kaczmarz Projection Algorithms with Rank Two Gain Update

Stotsky

2024

J Sign Process Syst

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New Kaczmarz algorithms with rank two gain update, extended orthogonality property and forgetting mechanism which includes both exponential and instantaneous forgetting (implemented via a proper choice of the forgetting factor and the window size) are introduced and systematically associated in this paper with well-known Kaczmarz algorithms with rank one update. The parameter convergence was proved using Lyapunov method and convergence of the inverse of the information matrix can be used for further performance improvement. The performance of new algorithms is examined in the problem of estimation of the grid events in the presence of significant harmonic emissions.

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Recursive versus nonrecursive Richardson algorithms: systematic overview, unified frameworks and application to electric grid power quality monitoring

Cited by 4 publications

References 19 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

Recursive Estimation in the Moving Window: Efficient Detection of the Distortions in the Grids with Desired Accuracy

Kaczmarz Projection Algorithms with Rank Two Gain Update

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