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Continuous-Time Varying Complex QR Decomposition via Zeroing Neural Dynamics

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Abstract

QR decomposition (QRD) is of fundamental importance for matrix factorization in both real and complex cases. In this paper, by using zeroing neural dynamics method, a continuous-time model is proposed for solving the time-varying problem of QRD in real-time. The proposed dynamics use time derivative information from a known real or complex matrix. Furthermore, its theoretical analysis is provided to substantiate the convergence and effectiveness of solving the time-varying QRD problem. In addition, numerical experiments in four different-dimensional time-varying matrices show that the proposed model is effective for solving the time-varying QRD problem both in the case of a real or a complex matrix as input.

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Acknowledgements

Predrag Stanimirović gratefully acknowledges support from the Ministry of Education, Science and Technological Development, Republic of Serbia, Grant No. 174013.

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Authors and Affiliations

  1. Division of Mathematics and Informatics, Department of Economics, National and Kapodistrian University of Athens, Sofokleous 1 Street, 10559, Athens, Greece

    Vasilios N. Katsikis & Spyridon D. Mourtas

  2. Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, 18000, Niš, Serbia

    Predrag S. Stanimirović

  3. School of Data and Computer Science, Sun Yat-sen University, Guangzhou, 510006, China

    Yunong Zhang

Authors
  1. Vasilios N. Katsikis
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  2. Spyridon D. Mourtas
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  3. Predrag S. Stanimirović
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  4. Yunong Zhang
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Correspondence to Vasilios N. Katsikis.

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Katsikis, V.N., Mourtas, S.D., Stanimirović, P.S. et al. Continuous-Time Varying Complex QR Decomposition via Zeroing Neural Dynamics. Neural Process Lett 53, 3573–3590 (2021). https://doi.org/10.1007/s11063-021-10566-y

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