Zeroing dynamics, gradient dynamics, and Newton iterations (Boca Raton, 2016). - ОГЛАВЛЕНИЕ / CONTENTS
Навигация
Архив выставки новых поступлений | Отечественные поступления | Иностранные поступления | Сиглы
ОбложкаZeroing dynamics, gradient dynamics, and Newton iterations / Y.Zhang et al. - Boca Raton: CRC/Taylor & Francis, 2016. - xxix, 309 p.: ill., tab. - Bibliogr.: p.297-305. - Ind.: p.307-309. - ISBN 978-1-4987-5376-0
Шифр: (И/В19-Z57) 02
 

Место хранения: 02 | Отделение ГПНТБ СО РАН | Новосибирск

Оглавление / Contents
 
List of Figures ................................................ xi
List of Tables ................................................ xix
Preface ....................................................... xxi
Author Biographies .......................................... xxvii
Acknowledgments .............................................. xxix

I  Time-Varying Root Finding .................................... 1
1  Time-Varying Square Root Finding ............................. 3
   1.1  Introduction ............................................ 3
   1.2  Problem Formulation and Continuous-Time (CT) Models ..... 4
   1.3  S-DTZD Model and Newton Iteration ....................... 7
   1.4  Illustrative Examples ................................... 8
   1.5  Summary ................................................ 12
2  Time-Varying Cube Root Finding .............................. 13
   2.1  Introduction ........................................... 13
   2.2  ZD Models for Time-Varying Case ........................ 14
   2.3  Simplified ZD Models for Constant Case and Newton 
        Iteration .............................................. 16
   2.4  Illustrative Examples .................................. 18
   2.5  Summary ................................................ 26
3  Time-Varying 4th Root Finding ............................... 27
   3.1  Introduction ........................................... 27
   3.2  Problem Formulation and ZD Models ...................... 28
   3.3  GD Model ............................................... 32
   3.4  Illustrative Examples .................................. 32
   3.5  Summary ................................................ 37
4  Time-Varying 5th Root Finding ............................... 39
   4.1  Introduction ........................................... 39
   4.2  ZD Models for Time-Varying Case ........................ 40
   4.3  Simplified ZD Models for Constant Case and Newton 
        Iteration .............................................. 43
   4.4  Illustrative Examples .................................. 44
   4.5  Summary ................................................ 49
   Appendix: Extension to Time-Varying pth Root Finding ........ 50

II  Nonlinear Equation Solving ................................. 53
5  Time-Varying Nonlinear Equation Solving ..................... 55
   5.1  Introduction ........................................... 55
   5.2  Problem Formulation and Solution Models ................ 56
   5.3  Convergence Analysis ................................... 57
   5.4  Illustrative Example ................................... 60
   5.5  Summary ................................................ 63
6  Static Nonlinear Equation Solving ........................... 65
   6.1  Problem Formulation and Continuous-Time Models ......... 66
   6.2  DTZD Models ............................................ 71
   6.3  Comparison between CTZD Model and Newton Iteration ..... 76
   6.4  Further Discussion to Avoid Local Minimum .............. 81
   6.5  Summary ................................................ 89
7  System of Nonlinear Equations Solving ....................... 91
   7.1  Problem Formulation and CTZD Model ..................... 91
   7.2  Discrete-Time Models ................................... 96
   7.3  Summary ............................................... 105

III  Matrix Inversion ......................................... 107
8  ZD Models and Newton Iteration ............................. 109
   8.1  Introduction .......................................... 109
   8.2  ZD Models ............................................. 110
   8.3  Choices of Initial State X0 ........................... 112
   8.4  Choices of Step Size h ................................ 116
   8.5  Illustrative Examples ................................. 121
   8.6  New DTZD Models Aided with Line-Search Algorithm ...... 124
   8.7  Summary ............................................... 130
9  Moore-Penrose Inversion .................................... 131
   9.1  Introduction .......................................... 131
   9.2  Preliminaries ......................................... 132
   9.3  ZD Models for Moore-Penrose Inverse ................... 133
   9.4  Comparison between ZD and GD Models ................... 137
   9.5  Simulation and Verification ........................... 139
   9.6  Application to Robot Arm .............................. 141
   9.7  Summary ............................................... 148

IV  Matrix Square Root Finding ................................ 149
10 ZD Models and Newton Iteration ............................. 151
   10.1 Introduction .......................................... 151
   10.2 Problem Formulation and ZD Models ..................... 152
   10.3 Link and Explanation to Newton Iteration .............. 156
   10.4 Line-Search Algorithm ................................. 157
   10.5 Illustrative Examples ................................. 158
   10.6 Summary ............................................... 160
11 ZD Model Using Hyperbolic Sine Activation Functions ........ 161
   11.1 Model and Activation Functions ........................ 161
   11.2 Convergence Analysis .................................. 162
   11.3 Robustness Analysis ................................... 166
   11.4 Illustrative Examples ................................. 167
   11.5 Summary ............................................... 175

V  Time-Varying Quadratic Optimization ........................ 177
12 ZD Models for Quadratic Minimization ....................... 179
   12.1 Introduction .......................................... 179
   12.2 Problem Formulation and CTZD Model .................... 180
   12.3 DTZD Models ........................................... 181
   12.4 GD Models ............................................. 182
   12.5 Illustrative Example .................................. 182
   12.6 Summary ............................................... 189
13 ZD Models for Quadratic Programming ........................ 191
   13.1 Introduction .......................................... 191
   13.2 CTZD Model ............................................ 192
   13.3 DTZD Models ........................................... 194
   13.4 Illustrative Examples ................................. 196
   13.5 Summary ............................................... 201
14 Simulative and Experimental Application to Robot Arms ...... 203
   14.1 Problem Formulation and Reformulation ................. 203
   14.2 Solution Models ....................................... 205
   14.3 Computer Simulations .................................. 206
   14.4 Hardware Experiments .................................. 210
   14.5 Summary ............................................... 215

VI Time-Varying Inequality Solving ............................ 217
15 Linear Inequality Solving .................................. 219
   15.1 Introduction .......................................... 220
   15.2 Time-Varying Linear Inequality ........................ 221
   15.3 Constant Linear Inequality ............................ 224
   15.4 Illustrative Examples ................................. 225
   15.5 System of Time-Varying Linear Inequalities ............ 229
   15.6 Illustrative Examples ................................. 239
   15.7 Summary ............................................... 253
16 System of Time-Varying Nonlinear Inequalities Solving ...... 255
   16.1 Introduction .......................................... 255
   16.2 Problem Formulation ................................... 257
   16.3 CZD Model and Convergence Analysis .................... 257
   16.4 MZD Model and Convergence Analysis .................... 259
   16.5 Illustrative Example .................................. 264
   16.6 Summary ............................................... 272

VII  Application to Fractals .................................. 273
17 Fractals Yielded via Static Nonlinear Equation ............. 275
   17.1 Introduction .......................................... 275
   17.2 Complex-Valued ZD Models .............................. 276
   17.3 Illustrative Examples ................................. 278
   17.4 Summary ............................................... 286
18 Fractals Yielded via Time-Varying Nonlinear Equation ....... 287
   18.1 Introduction .......................................... 287
   18.2 Complex-Valued ZD Models .............................. 288
   18.3 Illustrative Examples ................................. 291
   18.4 Summary ............................................... 294

Glossary ...................................................... 295
Bibliography .................................................. 297
Index ......................................................... 307

Архив выставки новых поступлений | Отечественные поступления | Иностранные поступления | Сиглы
 

[О библиотеке | Академгородок | Новости | Выставки | Ресурсы | Библиография | Партнеры | ИнфоЛоция | Поиск | English]
  Пожелания и письма: www@prometeus.nsc.ru
© 1997-2018 Отделение ГПНТБ СО РАН (Новосибирск)
Статистика доступов: архив | текущая статистика
 

Документ изменен: Thu Apr 5 17:11:42 2018. Размер: 12,841 bytes.
Посещение N 130 c 05.12.2017