Comprehensive Study on Zeroing Neural Network With High-Order Evolutionary Formula, Nonlinear Functions, and Variable Parameter for Time-Changing Matrix Cholesky Decomposition

In this article, a low-order zeroing neural network (LZNN), a high-order ZNN (HZNN), and a variable-parameter ZNN (VZNN) are designed and applied to the time-changing Cholesky decomposition of any positive-definite matrix, where the LZNN and HZNN models are generated based on the traditional and high-order evolutionary formulas, respectively. In addition, a new activation function (N-Acf) is applied to the LZNN, HZNN, and VZNN models to improve the convergence and robustness. Importantly, the LZNN and HZNN models activated by the N-Acf have faster predefined-time convergence velocity when solving the time-changing Cholesky decomposition problem of any positive-definite matrix, which is demonstrated via theoretical analysis and numerical experiments. Finally, in light of empirical and theoretical evidence, it can be established that the solution model of the VZNN model is able to undergo convergence to the theoretical solution of Cholesky decomposition despite the presence of interposing noise.