A class of quadratically convergent iterative methods

Predrag S. Stanimirović; Vasilios N. Katsikis; Shwetabh Srivastava; Dimitrios Pappas

Jerbi, H., Al-Darraji, I., Albadran, S., Aoun, S. B., Simos, T. E., Mourtas, S. D., & Katsikis, V. N. (2024). Solving quaternion nonsymmetric algebraic Riccati equations through zeroing neural networks. AIMS Mathematics, 9, 5794-5809. Website

Mourtas, S. D., Katsikis, V. N., Stanimirović, P. S., & Kazakovtsev, L. A. (2024). Credit and Loan Approval Classification Using a Bio-Inspired Neural Network. Biomimetics, 9. Website Abstract

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.

He, Y., Dong, X., Simos, T. E., Mourtas, S. D., Katsikis, V. N., Lagios, D., Zervas, P., et al. (2024). A bio-inspired weights and structure determination neural network for multiclass classification: Applications in occupational classification systems. AIMS Mathematics, 9, 2411-2434. Website

Jerbi, H., Alshammari, O., Aoun, S. B., Kchaou, M., Simos, T. E., Mourtas, S. D., & Katsikis, V. N. (2024). Hermitian Solutions of the Quaternion Algebraic Riccati Equations through Zeroing Neural Networks with Application to Quadrotor Control. Mathematics, 12. Website Abstract

The stability of nonlinear systems in the control domain has been extensively studied using different versions of the algebraic Riccati equation (ARE). This leads to the focus of this work: the search for the time-varying quaternion ARE (TQARE) Hermitian solution. The zeroing neural network (ZNN) method, which has shown significant success at solving time-varying problems, is used to do this. We present a novel ZNN model called ’ZQ-ARE’ that effectively solves the TQARE by finding only Hermitian solutions. The model works quite effectively, as demonstrated by one application to quadrotor control and three simulation tests. Specifically, in three simulation tests, the ZQ-ARE model finds the TQARE Hermitian solution under various initial conditions, and we also demonstrate that the convergence rate of the solution can be adjusted. Furthermore, we show that adapting the ZQ-ARE solution to the state-dependent Riccati equation (SDRE) technique stabilizes a quadrotor’s flight control system faster than the traditional differential-algebraic Riccati equation solution.

Gerontitis, D., Mo, C., Stanimirović, P. S., & Katsikis, V. N. (2024). Improved zeroing neural models based on two novel activation functions with exponential behavior. Theoretical Computer Science, 986, 114328. Website Abstract

A family of zeroing neural networks based on new nonlinear activation functions is proposed for solving various time-varying linear matrix equations (TVLME). The proposed neural network dynamical systems, symbolized as Li-VPZNN1 and Li-VPZNN2, include an exponential parameter in nonlinear activation function (AF) that leads to faster convergence to the theoretical result compared to previous categories of nonlinearly activated neural networks. Theoretical analysis as well as numerical tests in MATLAB's environment confirm the efficiency and accelerated convergence property of the novel dynamics.

Stanimirović, P. S., Mourtas, S. D., Mosić, D., Katsikis, V. N., Cao, X., & Li, S. (2024). Zeroing neural network approaches for computing time-varying minimal rank outer inverse. Applied Mathematics and Computation, 465, 128412. Website Abstract

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.

Gupta, R., Bartolucci, F., Katsikis, V. N., & Patnaik, S. (2023). Recent Advancements in Computational Finance and Business Analytics (1st ed., pp. 300). Springer Cham. Publisher's Version

Aoun, S. B., Derbel, N., Jerbi, H., Simos, T. E., Mourtas, S. D., & Katsikis., V. N. (2023). A quaternion Sylvester equation solver through noise-resilient zeroing neural networks with application to control the SFM chaotic system. AIMS Mathematics, 8(11). Publisher's Version

Cao, X., Peng, C., Zheng, Y., Li, S., Ha, T. T., Shutyaev, V., Katsikis, V. N., et al. (2023). Neural Networks for Portfolio Analysis in High-Frequency Trading. IEEE Transactions on Neural Networks and Learning Systems, 1-10.

Kovalnogov, V. N., Fedorov, R. V., Shepelev, I. I., Sherkunov, V. V., Simos, T. E., Mourtas, S. D., & Katsikis, V. N. (2023). A novel quaternion linear matrix equation solver through zeroing neural networks with applications to acoustic source tracking. AIMS Mathematics, 8, 25966-25989. Website Abstract

Due to its significance in science and engineering, time-varying linear matrix equation (LME) problems have received a lot of attention from scholars. It is for this reason that the issue of finding the minimum-norm least-squares solution of the time-varying quaternion LME (ML-TQ-LME) is addressed in this study. This is accomplished using the zeroing neural network (ZNN) technique, which has achieved considerable success in tackling time-varying issues. In light of that, two new ZNN models are introduced to solve the ML-TQ-LME problem for time-varying quaternion matrices of arbitrary dimension. Two simulation experiments and two practical acoustic source tracking applications show that the models function superbly.

Vasilios Katsikis

Professor, Economics

A class of quadratically convergent iterative methods

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