Gradient Neural Network with Nonlinear Activation for Computing Inner Inverses and the Drazin Inverse

被引：35

作者：

Stanimirovic, Predrag S. ^{[1
]}

Petkovic, Marko D. ^{[1
]}

Gerontitis, Dimitrios ^{[2
]}

机构：

[1] Univ Nis, Fac Sci & Math, Visegradska 33, Nish 18000, Serbia

[2] Aristotele Panepistim, Thessalonikis, Greece

来源：

NEURAL PROCESSING LETTERS | 2018年 / 48卷 / 01期

关键词：

Recurrent neural network; Moore-Penrose inverse; Drazin inverse; Dynamic equation; Activation function; ZNN MODELS; CONVERGENCE; DYNAMICS;

D O I：

10.1007/s11063-017-9705-4

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

Two gradient-based recurrent neural networks (GNNs) for solving two matrix equations are presented and investigated. These GNNs can be used for generating various inner inverses, including the Moore-Penrose, and in the computation of the Drazin inverse. Convergence properties of defined GNNs are considered. Certain conditions which impose convergence towards the pseudoinverse, and the Drazin inverse are exactly specified. The influence of nonlinear activation functions on the convergence performance of defined GNN models is investigated. Computer simulation experience further confirms the theoretical results.

引用

页码：109 / 133

页数：25

共 30 条

[21] Gradient-based Neural Network for Online Solution of Lyapunov Matrix Equation with Li Activation Function
Wang, Shiheng
Dai, Shidong
Wang, Ke
PROCEEDINGS OF THE 4TH INTERNATIONAL CONFERENCE ON INFORMATION TECHNOLOGY AND MANAGEMENT INNOVATION, 2015, 28 : 955 - 959
[22] Solving Quadratic Minimization Problem by Finite-Time Recurrent Neural Network Using Two Different Nonlinear Activation Functions
Zhang, Yongsheng
Xiao, Lin
Liao, Bolin
Ding, Lei
Lu, Rongbo
PROCEEDINGS OF 2018 TENTH INTERNATIONAL CONFERENCE ON ADVANCED COMPUTATIONAL INTELLIGENCE (ICACI), 2018, : 151 - 155
[23] Activation functions of artificial-neural-network-based nonlinear equalizers for optical nonlinearity compensation
Miyashita, Yuki
Kyono, Takeru
Ikuta, Kai
Kurokawa, Yuichiro
Nakamura, Moriya
IEICE COMMUNICATIONS EXPRESS, 2021, 10 (08): : 558 - 563
[24] A robust and fixed-time zeroing neural dynamics for computing time-variant nonlinear equation using a novel nonlinear activation function
Yu, Fei
Liu, Li
Xiao, Lin
Li, Kenli
Cai, Shuo
NEUROCOMPUTING, 2019, 350 : 108 - 116
[25] Gradient Descent-Barzilai Borwein-Based Neural Network Tracking Control for Nonlinear Systems With Unknown Dynamics
Wang, Yujia
Wang, Tong
Yang, Xuebo
Yang, Jiae
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, 2023, 34 (01) : 305 - 315
[26] Convergence of a Relaxed Variable Splitting Coarse Gradient Descent Method for Learning Sparse Weight Binarized Activation Neural Network
Dinh, Thu
Xin, Jack
FRONTIERS IN APPLIED MATHEMATICS AND STATISTICS, 2020, 6
[27] FPGA implementation and image encryption application of a new PRNG based on a memristive Hopfield neural network with a special activation gradient
Yu, Fei
Zhang, Zinan
Shen, Hui
Huang, Yuanyuan
Cai, Shuo
Du, Sichun
CHINESE PHYSICS B, 2022, 31 (02)
[28] A nonlinear zeroing neural network and its applications on time-varying linear matrix equations solving, electronic circuit currents computing and robotic manipulator trajectory tracking
Jin, Jie
Chen, Weijie
Zhao, Lv
Chen, Long
Tang, Zhijun
COMPUTATIONAL & APPLIED MATHEMATICS, 2022, 41 (07)
[29] Adaptive Coefficient Designs for Nonlinear Activation Function and Its Application to Zeroing Neural Network for Solving Time-Varying Sylvester Equation
Jian, Zhen
Xiao, Lin
Li, Kenli
Zuo, Qiuyue
Zhang, Yongsheng
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 2020, 357 (14): : 9909 - 9929
[30] Discrete gradient-zeroing neural network algorithm for solving future Sylvester equation aided with left-right four-step rule as well as robot arm inverse kinematics
Guo, Pengfei
Zhang, Yunong
Yao, Zheng-an
MATHEMATICS AND COMPUTERS IN SIMULATION, 2025, 233 : 475 - 501

← 1 2 3 →