Bounded Adaptive Function Activated Recurrent Neural Network for Solving the Dynamic QR Factorization

Wenrui Yang, Yang Gu, Xia Xie (), Chengze Jiang, Zhiyuan Song and Yudong Zhang
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Wenrui Yang: School of Computer Science and Technology, Hainan University, Haikou 570228, China
Yang Gu: School of Computer Science and Technology, Hainan University, Haikou 570228, China
Xia Xie: School of Computer Science and Technology, Hainan University, Haikou 570228, China
Chengze Jiang: School of Cyber Science and Engineering, Southeast University, Nanjing 211189, China
Zhiyuan Song: School of Electronics and Information Engineering, Guangdong Ocean University, Zhanjiang 524088, China
Yudong Zhang: School of Computing and Mathematical Sciences, University of Leicester, Leicester LE1 7RH, UK

Mathematics, 2023, vol. 11, issue 10, 1-18

Abstract: The orthogonal triangular factorization (QRF) method is a widespread tool to calculate eigenvalues and has been used for many practical applications. However, as an emerging topic, only a few works have been devoted to handling dynamic QR factorization (DQRF). Moreover, the traditional methods for dynamic problems suffer from lagging errors and are susceptible to noise, thereby being unable to satisfy the requirements of the real-time solution. In this paper, a bounded adaptive function activated recurrent neural network (BAFARNN) is proposed to solve the DQRF with a faster convergence speed and enhance existing solution methods’ robustness. Theoretical analysis shows that the model can achieve global convergence in different environments. The results of the systematic experiment show that the BAFARNN model outperforms both the original ZNN (OZNN) model and the noise-tolerant zeroing neural network (NTZNN) model in terms of accuracy and convergence speed. This is true for both single constants and time-varying noise disturbances.

Keywords: recurrent neural network; adaptive coefficient; QR factorization; time-varying matrix (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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