Zeroing Dynamics, Gradient Dynamics, and Newton Iterations (Hardcover)
暫譯: 零化動力學、梯度動力學與牛頓迭代法 (精裝版)

Yunong Zhang, Lin Xiao, Zhengli Xiao, Mingzhi Mao

  • 出版商: CRC
  • 出版日期: 2015-12-01
  • 售價: $6,660
  • 貴賓價: 9.5$6,327
  • 語言: 英文
  • 頁數: 340
  • 裝訂: Hardcover
  • ISBN: 1498753760
  • ISBN-13: 9781498753760
  • 海外代購書籍(需單獨結帳)

相關主題

商品描述

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.

商品描述(中文翻譯)

神經網絡和神經動力學是解決科學、工程和商業中出現的數學問題的強大方法。與僅處理常數係數矩陣和向量的靜態問題的傳統梯度神經網絡相比,作者提出的新方法稱為零化動力學,能夠解決隨時間變化的問題。

《零化動力學、梯度動力學與牛頓迭代》是第一本展示如何準確且高效地使用連續或離散時間的零化動力學在實時或在線解決隨時間變化問題的書籍。這本書匯集了神經網絡、神經動力學、計算數學、數值算法、隨時間變化的計算與優化、模擬與建模、類比與數位硬體以及分形等新興領域的研究。

作者對靜態和動態神經網絡的理論進行了全面的闡述。讀者將發現新穎的理論結果如何成功應用於許多實際問題。作者開發、分析、建模、模擬並比較零化動力學模型,以在線解決多個隨時間變化的問題,例如根尋找、非線性方程求解、矩陣反演、矩陣平方根尋找、二次優化和不等式求解。