Real-Domain QR Decomposition Models Employing Zeroing Neural Network and Time-Discretization Formulas for Time-Varying Matrices

Li, Zhenyu; Zhang, Yunong; Ming, Liangjie; Guo, Jinjin; Vasilios N. Katsikis

Real-Domain QR Decomposition Models Employing Zeroing Neural Network and Time-Discretization Formulas for Time-Varying Matrices

Citation:

Li, Z., Zhang, Y., Ming, L., Guo, J., & Katsikis, V. N. (2021). Real-Domain QR Decomposition Models Employing Zeroing Neural Network and Time-Discretization Formulas for Time-Varying Matrices. Neurocomputing. presented at the 2021. Copy at http://www.tinyurl.com/ygsjszu9

Abstract:

This study investigated the problem of QR decomposition for time-varying matrices. We transform the original QR decomposition problem into an equation system using its constraints. Then, we propose a continuous-time QR decomposition (CTQRD) model by applying zeroing neural network method, equivalent transformations, Kronecker product, and vectorization techniques. Subsequently, a high-precision ten-instant Zhang et al discretization (ZeaD) formula is proposed. A ten-instant discrete-time QR decomposition model is also proposed by using the ten-instant ZeaD formula to discretize the CTQRD model. Moreover, three discrete-time QR decomposition models are proposed by applying three other ZeaD formulas, and three examples of QR decomposition are presented. The experimental results confirm the effectiveness and correctness of the proposed models for the QR decomposition of time-varying matrices.

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Contact Details

National and Kapodistrian University of Athens
Office: 601 (Floor 6)
Phone number: (+30) 210-3689489
Address: Sofokleous 1, 10559, Athens, Greece
Email: vaskatsikis@econ.uoa.gr
URL: http://scholar.uoa.gr/vaskatsikis
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Recent Publications

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Numerous people are applying for bank loans as a result of the banking industry’s expansion, but because banks only have a certain amount of assets to lend to, they can only do so to a certain number of applicants. Therefore, the banking industry is very interested in finding ways to reduce the risk factor involved in choosing the safe applicant in order to save lots of bank resources. These days, machine learning greatly reduces the amount of work needed to choose the safe applicant. Taking this into account, a novel weights and structure determination (WASD) neural network has been built to meet the aforementioned two challenges of credit approval and loan approval, as well as to handle the unique characteristics of each. Motivated by the observation that WASD neural networks outperform conventional back-propagation neural networks in terms of sluggish training speed and being stuck in local minima, we created a bio-inspired WASD algorithm for binary classification problems (BWASD) for best adapting to the credit or loan approval model by utilizing the metaheuristic beetle antennae search (BAS) algorithm to improve the learning procedure of the WASD algorithm. Theoretical and experimental study demonstrate superior performance and problem adaptability. Furthermore, we provide a complete MATLAB package to support our experiments together with full implementation and extensive installation instructions.

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Generalized inverses are extremely effective in many areas of mathematics and engineering. The zeroing neural network (ZNN) technique, which is currently recognized as the state-of-the-art approach for calculating the time-varying Moore-Penrose matrix inverse, is investigated in this study as a solution to the problem of calculating the time-varying minimum rank outer inverse (TV-MROI) with prescribed range and/or TV-MROI with prescribed kernel. As a result, four novel ZNN models are introduced for computing the TV-MROI, and their efficiency is examined. Numerical tests examine and validate the effectiveness of the introduced ZNN models for calculating TV-MROI with prescribed range and/or prescribed kernel.

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Vasilios Katsikis

Professor, Economics

Real-Domain QR Decomposition Models Employing Zeroing Neural Network and Time-Discretization Formulas for Time-Varying Matrices

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