Theoretical and computational improvements to the algebraic method for discovering cooperative rigid-unit modes

A linear-algebraic algorithm for identifying rigid-unit modes in networks of interconnected rigid units has recently been demonstrated. This article presents a series of enhancements to the original algorithm, which greatly improve its conceptual simplicity, numerical robustness, computational efficiency and interpretability. The improvements include the efficient isolation of constraints, the observation of variable-block separability, the use of singular value decomposition and a quantitative measure of solution inexactness.

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Method for Clustering Daily Load Curve Based on SVD-KICIC

Energies ◽

10.3390/en13174476 ◽

2020 ◽

Vol 13 (17) ◽

pp. 4476

Author(s):

Yikun Zhang ◽

Jing Zhang ◽

Gang Yao ◽

Xiao Xu ◽

Kewen Wei

Keyword(s):

Singular Value Decomposition ◽

Computational Efficiency ◽

Clustering Algorithm ◽

Operation Time ◽

Singular Values ◽

Singular Value ◽

Load Curve ◽

Clustering Quality ◽

Value Decomposition ◽

Daily Load

Clustering electric load curves is an important part of the load data mining process. In this paper, we propose a clustering algorithm by combining singular value decomposition and KICIC clustering algorithm (SVD-KICIC) for analyzing the characteristics of daily load curves to mitigate some of the traditional clustering algorithm problems, such as only considering intra-class distance and low computational efficiency when dealing with massive load data. Our method identifies effective daily load curve characteristics using the singular value decomposition technique to improve dimensionality reduction, which improves low computational efficiency by reducing the number of dimensions inherent in big data. Additionally, the method performs SVD on the load data to obtain singular values for determination of weight of the KICIC algorithm, which leverages intra-class and inter-class distances of the load data and further improves the computational efficiency of the algorithm. Finally, we perform a series of simulations of actual load curves from a certain city to validate that the algorithm proposed in this paper has a short operation time, high clustering quality, and solid robustness that improves the clustering performance of the load curves.

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Improved Iterative Coordinated Beamforming Based on Singular Value Decomposition for Multiuser Mimo Systems With Limited Feedforward

Journal of Applied Research and Technology ◽

10.22201/icat.16656423.2011.9.03.429 ◽

2011 ◽

Vol 9 (03) ◽

Author(s):

L. Soriano-Equigua ◽

J. Sánchez-García ◽

C.B. Chae ◽

R. W. Heath Jr

Keyword(s):

Singular Value Decomposition ◽

Bit Error Rate ◽

Error Rate ◽

Base Station ◽

Wireless Channel ◽

Singular Value ◽

Coordinated Beamforming ◽

Original Algorithm ◽

Value Decomposition ◽

Number Of Iterations

Coordinated beamforming based on singular value decomposition is an iterative method to jointly optimize the transmit beamformers and receive combiners, to achieve high levels of sum rates in the downlink of multiuser systems, by exploiting the multi-dimensional wireless channel created by multiple transmit and receive antennas. The optimization is done at the base station and the quantized beamformers are sent to the users through a low rate link.In this work, we propose to optimize this algorithm by reducing the number of iterations and improving its uncoded bit error rate performance. Simulation results show that our proposal achieves a better bit error rate with a lower number of iterations than the original algorithm.

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