可列斯基分解
最小度算法
人工神经网络
基质(化学分析)
变量(数学)
分解
非线性系统
应用数学
数学
计算机科学
数学优化
算法
不完全Cholesky因式分解
数学分析
人工智能
物理
材料科学
生物
特征向量
复合材料
量子力学
生态学
作者
Lin Xiao,Sida Xiao,Yongjun He,Jianhua Dai,Yaonan Wang,Yiwei Li
标识
DOI:10.1109/tsmc.2024.3370636
摘要
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.
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