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Journal articles on the topic 'Matrix pseudoinversion'

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Author: Grafiati

Published: 11 March 2023

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1

Kornilova, Mariya, Vladislav Kovalnogov, Ruslan Fedorov, Mansur Zamaleev, Vasilios N. Katsikis, Spyridon D. Mourtas, and Theodore E. Simos. "Zeroing Neural Network for Pseudoinversion of an Arbitrary Time-Varying Matrix Based on Singular Value Decomposition." Mathematics 10, no. 8 (April 7, 2022): 1208. http://dx.doi.org/10.3390/math10081208.

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Many researchers have investigated the time-varying (TV) matrix pseudoinverse problem in recent years, for its importance in addressing TV problems in science and engineering. In this paper, the problem of calculating the inverse or pseudoinverse of an arbitrary TV real matrix is considered and addressed using the singular value decomposition (SVD) and the zeroing neural network (ZNN) approaches. Since SVD is frequently used to compute the inverse or pseudoinverse of a matrix, this research proposes a new ZNN model based on the SVD method as well as the technique of Tikhonov regularization, for solving the problem in continuous time. Numerical experiments, involving the pseudoinversion of square, rectangular, singular, and nonsingular input matrices, indicate that the proposed models are effective for solving the problem of the inversion or pseudoinversion of time varying matrices.

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2

Kononov, M. V., O. A. Nagulyak, A. V. Netreba, and A. A. Sudakov. "Reconstruction in NMR by the method of signal matrix pseudoinversion." Radioelectronics and Communications Systems 51, no. 10 (October 2008): 531–33. http://dx.doi.org/10.3103/s0735272708100038.

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3

Xiang, Qiuhong, Bolin Liao, Lin Xiao, Long Lin, and Shuai Li. "Discrete-time noise-tolerant Zhang neural network for dynamic matrix pseudoinversion." Soft Computing 23, no. 3 (March 8, 2018): 755–66. http://dx.doi.org/10.1007/s00500-018-3119-8.

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4

Stanimirović, Predrag S., Spyridon D. Mourtas, Vasilios N. Katsikis, Lev A. Kazakovtsev, and Vladimir N. Krutikov. "Recurrent Neural Network Models Based on Optimization Methods." Mathematics 10, no. 22 (November 16, 2022): 4292. http://dx.doi.org/10.3390/math10224292.

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Many researchers have addressed problems involving time-varying (TV) general linear matrix equations (GLMEs) because of their importance in science and engineering. This research discusses and solves the topic of solving TV GLME using the zeroing neural network (ZNN) design. Five new ZNN models based on novel error functions arising from gradient-descent and Newton optimization methods are presented and compared to each other and to the standard ZNN design. Pseudoinversion is involved in four proposed ZNN models, while three of them are related to Newton’s optimization method. Heterogeneous numerical examples show that all models successfully solve TV GLMEs, although their effectiveness varies and depends on the input matrix.

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5

Liao, Bolin, and Qiuhong Xiang. "Robustness Analyses and Optimal Sampling Gap of Recurrent Neural Network for Dynamic Matrix Pseudoinversion." Journal of Advanced Computational Intelligence and Intelligent Informatics 21, no. 5 (September 20, 2017): 778–84. http://dx.doi.org/10.20965/jaciii.2017.p0778.

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This study analyses the robustness and convergence characteristics of a neural network. First, a special class of recurrent neural network (RNN), termed a continuous-time Zhang neural network (CTZNN) model, is presented and investigated for dynamic matrix pseudoinversion. Theoretical analysis of the CTZNN model demonstrates that it has good robustness against various types of noise. In addition, considering the requirements of digital implementation and online computation, the optimal sampling gap for a discrete-time Zhang neural network (DTZNN) model under noisy environments is proposed. Finally, experimental results are presented, which further substantiate the theoretical analyses and demonstrate the effectiveness of the proposed ZNN models for computing a dynamic matrix pseudoinverse under noisy environments.

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6

Alharbi, Hadeel, Houssem Jerbi, Mourad Kchaou, Rabeh Abbassi, Theodore E. Simos, Spyridon D. Mourtas, and Vasilios N. Katsikis. "Time-Varying Pseudoinversion Based on Full-Rank Decomposition and Zeroing Neural Networks." Mathematics 11, no. 3 (January 24, 2023): 600. http://dx.doi.org/10.3390/math11030600.

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The computation of the time-varying matrix pseudoinverse has become crucial in recent years for solving time-varying problems in engineering and science domains. This paper investigates the issue of calculating the time-varying pseudoinverse based on full-rank decomposition (FRD) using the zeroing neural network (ZNN) method, which is currently considered to be a cutting edge method for calculating the time-varying matrix pseudoinverse. As a consequence, for the first time in the literature, a new ZNN model called ZNNFRDP is introduced for time-varying pseudoinversion and it is based on FRD. FourFive numerical experiments investigate and confirm that the ZNNFRDP model performs as well as, if not better than, other well-performing ZNN models in the calculation of the time-varying pseudoinverse. Additionally, theoretical analysis and numerical findings have both supported the effectiveness of the proposed model.

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7

Hu, Zeshan, Lin Xiao, Kenli Li, Keqin Li, and Jichun Li. "Performance analysis of nonlinear activated zeroing neural networks for time-varying matrix pseudoinversion with application." Applied Soft Computing 98 (January 2021): 106735. http://dx.doi.org/10.1016/j.asoc.2020.106735.

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8

Kohno, Kiyotaka, Mitsuru Kawamoto, and Yujiro Inouye. "A Matrix Pseudoinversion Lemma and Its Application to Block-Based Adaptive Blind Deconvolution for MIMO Systems." IEEE Transactions on Circuits and Systems I: Regular Papers 57, no. 7 (July 2010): 1449–62. http://dx.doi.org/10.1109/tcsi.2010.2050222.

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9

Jin, Long, Shuai Li, Huanqing Wang, and Zhijun Zhang. "Nonconvex projection activated zeroing neurodynamic models for time-varying matrix pseudoinversion with accelerated finite-time convergence." Applied Soft Computing 62 (January 2018): 840–50. http://dx.doi.org/10.1016/j.asoc.2017.09.016.

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10

Simos, Theodore E., Vasilios N. Katsikis, Spyridon D. Mourtas, Predrag S. Stanimirović, and Dimitris Gerontitis. "A higher-order zeroing neural network for pseudoinversion of an arbitrary time-varying matrix with applications to mobile object localization." Information Sciences 600 (July 2022): 226–38. http://dx.doi.org/10.1016/j.ins.2022.03.094.

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11

Jin, Long, and Yunong Zhang. "Discrete-time Zhang neural network of O(τ3) pattern for time-varying matrix pseudoinversion with application to manipulator motion generation." Neurocomputing 142 (October 2014): 165–73. http://dx.doi.org/10.1016/j.neucom.2014.04.051.

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12

Guo, Dongsheng, and Yunong Zhang. "Li-function activated ZNN with finite-time convergence applied to redundant-manipulator kinematic control via time-varying Jacobian matrix pseudoinversion." Applied Soft Computing 24 (November 2014): 158–68. http://dx.doi.org/10.1016/j.asoc.2014.06.045.

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13

Liao, Bolin, and Yunong Zhang. "From different ZFs to different ZNN models accelerated via Li activation functions to finite-time convergence for time-varying matrix pseudoinversion." Neurocomputing 133 (June 2014): 512–22. http://dx.doi.org/10.1016/j.neucom.2013.12.001.

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14

Liao, Bolin, Yuyan Wang, Jianfeng Li, Dongsheng Guo, and Yongjun He. "Harmonic Noise-Tolerant ZNN for Dynamic Matrix Pseudoinversion and Its Application to Robot Manipulator." Frontiers in Neurorobotics 16 (June 13, 2022). http://dx.doi.org/10.3389/fnbot.2022.928636.

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As we know, harmonic noises widely exist in industrial fields and have a crucial impact on the computational accuracy of the zeroing neural network (ZNN) model. For tackling this issue, by combining the dynamics of harmonic signals, two harmonic noise-tolerant ZNN (HNTZNN) models are designed for the dynamic matrix pseudoinversion. In the design of HNTZNN models, an adaptive compensation term is adopted to eliminate the influence of harmonic noises, and a Li activation function is introduced to further improve the convergence rate. The convergence and robustness to harmonic noises of the proposed HNTZNN models are proved through theoretical analyses. Besides, compared with the ZNN model without adaptive compensation term, the HNTZNN models are more effective for tacking the problem of dynamic matrix pseudoinverse under harmonic noises environments. Moreover, HNTZNN models are further applied to the kinematic control of a four-link planar robot manipulator under harmonic noises. In general, the experimental results verify the effectiveness, superiority, and broad application prospect of the models.

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15

Huang, Haoen, Dongyang Fu, Xiuchun Xiao, Yangyang Ning, Huan Wang, Long Jin, and Shan Liao. "Modified Newton Integration Neural Algorithm for Dynamic Complex-Valued Matrix Pseudoinversion Applied to Mobile Object Localization." IEEE Transactions on Industrial Informatics, 2020, 1. http://dx.doi.org/10.1109/tii.2020.3005937.

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