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Zeroing Dynamics, Gradient Dynamics, and Newton Iterations [Kõva köide]

(Sun Yat-sen University, Guangzhou, Guangdong, China), (Jishou University, Hunan, China), (Sun Yat-sen University, Guangzhou, Guangdong, China), (Sun Yat-sen University, Guangzhou, Guangdong, China)
  • Formaat: Hardback, 310 pages, kõrgus x laius: 254x178 mm, kaal: 771 g, 22 Tables, black and white; 294 Illustrations, black and white
  • Ilmumisaeg: 01-Dec-2015
  • Kirjastus: CRC Press Inc
  • ISBN-10: 1498753760
  • ISBN-13: 9781498753760
Teised raamatud teemal:
Zeroing Dynamics, Gradient Dynamics, and Newton IterationsSuurem pilt
  • Formaat: Hardback, 310 pages, kõrgus x laius: 254x178 mm, kaal: 771 g, 22 Tables, black and white; 294 Illustrations, black and white
  • Ilmumisaeg: 01-Dec-2015
  • Kirjastus: CRC Press Inc
  • ISBN-10: 1498753760
  • ISBN-13: 9781498753760
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781498753760.html
Märksõnad:
Neural networks and neural dynamics are powerful approaches for the online solution of mathematical problems arising in many areas of science, engineering, and business. Compared with conventional gradient neural networks that only deal with static problems of constant coefficient matrices and vectors, the authors new method called zeroing dynamics solves time-varying problems.

Zeroing Dynamics, Gradient Dynamics, and Newton Iterations is the first book that shows how to accurately and efficiently solve time-varying problems in real-time or online using continuous- or discrete-time zeroing dynamics. The book brings together research in the developing fields of neural networks, neural dynamics, computer mathematics, numerical algorithms, time-varying computation and optimization, simulation and modeling, analog and digital hardware, and fractals.

The authors provide a comprehensive treatment of the theory of both static and dynamic neural networks. Readers will discover how novel theoretical results have been successfully applied to many practical problems. The authors develop, analyze, model, simulate, and compare zeroing dynamics models for the online solution of numerous time-varying problems, such as root finding, nonlinear equation solving, matrix inversion, matrix square root finding, quadratic optimization, and inequality solving.
List of Figures
xi
List of Tables
xix
Preface xxi
Author Biographies xxvii
Acknowledgments xxix
I Time-Varying Root Finding
1(52)
1 Time-Varying Square Root Finding
3(10)
1.1 Introduction
3(1)
1.2 Problem Formulation and Continuous-Time (CT) Models
4(3)
1.3 S-DTZD Model and Newton Iteration
7(1)
1.4 Illustrative Examples
8(4)
1.5 Summary
12(1)
2 Time-Varying Cube Root Finding
13(14)
2.1 Introduction
13(1)
2.2 ZD Models for Time-Varying Case
14(2)
2.3 Simplified ZD Models for Constant Case and Newton Iteration
16(2)
2.4 Illustrative Examples
18(8)
2.5 Summary
26(1)
3 Time-Varying 4th Root Finding
27(12)
3.1 Introduction
27(1)
3.2 Problem Formulation and ZD Models
28(4)
3.3 GD Model
32(1)
3.4 Illustrative Examples
32(5)
3.5 Summary
37(2)
4 Time-Varying 5th Root Finding
39(14)
4.1 Introduction
39(1)
4.2 ZD Models for Time-Varying Case
40(3)
4.3 Simplified ZD Models for Constant Case and Newton Iteration
43(1)
4.4 Illustrative Examples
44(5)
4.5 Summary
49(4)
Appendix: Extension to Time-Varying ρth Root Finding
50(3)
II Nonlinear Equation Solving
53(54)
5 Time-Varying Nonlinear Equation Solving
55(10)
5.1 Introduction
55(1)
5.2 Problem Formulation and Solution Models
56(1)
5.3 Convergence Analysis
57(3)
5.4 Illustrative Example
60(3)
5.5 Summary
63(2)
6 Static Nonlinear Equation Solving
65(26)
6.1 Problem Formulation and Continuous-Time Models
66(5)
6.2 DTZD Models
71(5)
6.3 Comparison between CTZD Model and Newton Iteration
76(5)
6.4 Further Discussion to Avoid Local Minimum
81(8)
6.5 Summary
89(2)
7 System of Nonlinear Equations Solving
91(16)
7.1 Problem Formulation and CTZD Model
91(5)
7.2 Discrete-Time Models
96(9)
7.3 Summary
105(2)
III Matrix Inversion
107(42)
8 ZD Models and Newton Iteration
109(22)
8.1 Introduction
109(1)
8.2 ZD Models
110(2)
8.3 Choices of Initial State X0
112(4)
8.4 Choices of Step Size h
116(5)
8.5 Illustrative Examples
121(3)
8.6 New DTZD Models Aided with Line-Search Algorithm
124(6)
8.7 Summary
130(1)
9 Moore--Penrose Inversion
131(18)
9.1 Introduction
131(1)
9.2 Preliminaries
132(1)
9.3 ZD Models for Moore--Penrose Inverse
133(4)
9.4 Comparison between ZD and GD Models
137(2)
9.5 Simulation and Verification
139(2)
9.6 Application to Robot Arm
141(7)
9.7 Summary
148(1)
IV Matrix Square Root Finding
149(28)
10 ZD Models and Newton Iteration
151(10)
10.1 Introduction
151(1)
10.2 Problem Formulation and ZD Models
152(4)
10.3 Link and Explanation to Newton Iteration
156(1)
10.4 Line-Search Algorithm
157(1)
10.5 Illustrative Examples
158(2)
10.6 Summary
160(1)
11 ZD Model Using Hyperbolic Sine Activation Functions
161(16)
11.1 Model and Activation Functions
161(1)
11.2 Convergence Analysis
162(4)
11.3 Robustness Analysis
166(1)
11.4 Illustrative Examples
167(8)
11.5 Summary
175(2)
V Time-Varying Quadratic Optimization
177(40)
12 ZD Models for Quadratic Minimization
179(12)
12.1 Introduction
179(1)
12.2 Problem Formulation and CTZD Model
180(1)
12.3 DTZD Models
181(1)
12.4 GD Models
182(1)
12.5 Illustrative Example
182(7)
12.6 Summary
189(2)
13 ZD Models for Quadratic Programming
191(12)
13.1 Introduction
191(1)
13.2 CTZD Model
192(2)
13.3 DTZD Models
194(2)
13.4 Illustrative Examples
196(5)
13.5 Summary
201(2)
14 Simulative and Experimental Application to Robot Arms
203(14)
14.1 Problem Formulation and Reformulation
203(2)
14.2 Solution Models
205(1)
14.3 Computer Simulations
206(4)
14.4 Hardware Experiments
210(5)
14.5 Summary
215(2)
VI Time-Varying Inequality Solving
217(56)
15 Linear Inequality Solving
219(36)
15.1 Introduction
220(1)
15.2 Time-Varying Linear Inequality
221(3)
15.3 Constant Linear Inequality
224(1)
15.4 Illustrative Examples
225(4)
15.5 System of Time-Varying Linear Inequalities
229(10)
15.6 Illustrative Examples
239(14)
15.7 Summary
253(2)
16 System of Time-Varying Nonlinear Inequalities Solving
255(18)
16.1 Introduction
255(2)
16.2 Problem Formulation
257(1)
16.3 CZD Model and Convergence Analysis
257(2)
16.4 MZD Model and Convergence Analysis
259(5)
16.5 Illustrative Example
264(8)
16.6 Summary
272(1)
VII Application to Fractals
273(22)
17 Fractals Yielded via Static Nonlinear Equation
275(12)
17.1 Introduction
275(1)
17.2 Complex-Valued ZD Models
276(2)
17.3 Illustrative Examples
278(8)
17.4 Summary
286(1)
18 Fractals Yielded via Time-Varying Nonlinear Equation
287(8)
18.1 Introduction
287(1)
18.2 Complex-Valued ZD Models
288(3)
18.3 Illustrative Examples
291(3)
18.4 Summary
294(1)
Glossary 295(2)
Bibliography 297(10)
Index 307
Yunong Zhang is a professor in the School of Information Science and Technology at Sun Yat-sen University. He is also with the SYSU-CMU Shunde International Joint Research Institute for cooperative research. He has published more than 375 scientific works of various types and has been a winner of the Best Paper Award of ISSCAA and the Best Paper Award of ICAL. He was among the 2014 Highly Cited Scholars of China. His main research interests include neural networks, robotics, computation, and optimization. He earned a PhD from the Chinese University of Hong Kong.

Lin Xiao is a lecturer in the College of Information Science and Engineering at Jishou University. His current research interests include neural networks, intelligent information processing, robotics, and related areas. He earned a PhD from Sun Yat-sen University.

Zhengli Xiao is currently pursuing an MS in the Department of Computer Science in the School of Information Science and Technology at Sun Yat-sen University. He is also with the SYSU-CMU Shunde International Joint Research Institute for cooperative research. His current research interests include neural networks, intelligent information processing, and learning machines. He earned a BS in software engineering from Changchun University of Science and Technology.

Mingzhi Mao is an associate professor in the School of Information Science and Technology at Sun Yat-sen University. His main research interests include intelligence algorithms, software engineering, and management information systems. He earned a PhD from the Department of Computer Science at Sun Yat-sen University.