ABSTRACT
Calculation of the time-varying (TV) matrix generalized inverse has grown into an essential tool in many fields, such as computer science, physics, engineering, and mathematics, in order to tackle TV challenges. This work investigates the challenge of finding a TV extension of a subclass of inner inverses on real matrices, known as generalized-outer (G-outer) inverses. More precisely, our goal is to construct TV G-outer inverses (TV-GOIs) by utilizing the zeroing neural network (ZNN) process, which is presently thought to be a state-of-the-art solution to tackling TV matrix challenges. Using known advantages of ZNN dynamic systems, a novel ZNN model, called ZNNGOI, is presented in the literature for the first time in order to compute TV-GOIs. The ZNNGOI performs excellently in performed numerical simulations and an application on addressing localization problems. In terms of solving linear TV matrix equations, its performance is comparable to that of the standard ZNN model for computing the pseudoinverse.
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.
ABSTRACT
The problem of solving linear equations is considered as one of the fundamental problems commonly encountered in science and engineering. In this article, the complex-valued time-varying linear matrix equation (CVTV-LME) problem is investigated. Then, by employing a complex-valued, time-varying QR (CVTVQR) decomposition, the zeroing neural network (ZNN) method, equivalent transformations, Kronecker product, and vectorization techniques, we propose and study a CVTVQR decomposition-based linear matrix equation (CVTVQR-LME) model. In addition to the usage of the QR decomposition, the further advantage of the CVTVQR-LME model is reflected in the fact that it can handle a linear system with square or rectangular coefficient matrix in both the matrix and vector cases. Its efficacy in solving the CVTV-LME problems have been tested in a variety of numerical simulations as well as in two applications, one in robotic motion tracking and the other in angle-of-arrival localization.
