Generalized Matrix Inversion: A Machine Learning Approach
暫譯: 廣義矩陣反演：機器學習方法

Stanimirovic, Predrag S., Wei, Yimin, Li, Shuai

Generalized Matrix Inversion: A Machine Learning Approach
  • 出版商: Springer
  • 出版日期: 2026-01-03
  • 售價: $8,900
  • 貴賓價: 9.5 折 $8,455
  • 語言: 英文
  • 頁數: 333
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 3032014921
  • ISBN-13: 9783032014924
  • 相關分類: Machine Learning

    • 海外代購書籍(需單獨結帳)

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商品描述

This book presents a comprehensive exploration of the dynamical system approach in numerical linear algebra, with a special focus on computing generalized inverses, solving systems of linear equations, and addressing linear matrix equations. Bridging four major scientific domains--numerical linear algebra, recurrent neural networks (RNNs), dynamical systems, and unconstrained nonlinear optimization--this book offers a unique, interdisciplinary perspective.

Generalized Matrix Inversion: A Machine Learning Approach explores the theory and application of recurrent neural networks, particularly continuous-time recurrent neural networks (CTRNNs), which use systems of ordinary differential equations to model the influence of inputs on neurons. Special attention is given to CTRNNs designed for finding zeros of equations or minimizing nonlinear functions, with detailed coverage of two important classes: Gradient Neural Networks (GNN) and Zhang (Zeroing) Neural Networks (ZNN). Both time-varying and time-invariant models are examined across scalar, vector, and matrix cases.

Based on the authors' research that has been published in leading scientific journals, the book spans a variety of disciplines, including linear and multilinear algebra, generalized inverses, recurrent neural networks, dynamical systems, time-varying problem solving, and unconstrained nonlinear optimization. Readers will find a global overview of activation functions, rigorous convergence analysis, and innovative improvements in the definition of error functions for GNN and ZNN dynamic systems.

Generalized Matrix Inversion: A Machine Learning Approach is an essential resource for researchers and practitioners seeking advanced methods at the intersection of machine learning, optimization, and matrix computation.

商品描述(中文翻譯)

本書全面探討了數值線性代數中的動態系統方法，特別關注於計算廣義逆、解線性方程組以及處理線性矩陣方程。該書橋接了四個主要的科學領域——數值線性代數、遞迴神經網絡（RNNs）、動態系統和無約束非線性優化，提供了一個獨特的跨學科視角。

《廣義矩陣逆：機器學習方法》探討了遞迴神經網絡的理論和應用，特別是連續時間遞迴神經網絡（CTRNNs），這些網絡使用常微分方程系統來建模輸入對神經元的影響。特別關注於設計用於尋找方程零點或最小化非線性函數的CTRNN，詳細涵蓋了兩個重要類別：梯度神經網絡（GNN）和張（零點）神經網絡（ZNN）。本書檢視了標量、向量和矩陣情況下的時間變化和時間不變模型。

基於作者在領先科學期刊上發表的研究，本書涵蓋了多個學科，包括線性和多線性代數、廣義逆、遞迴神經網絡、動態系統、時間變化問題解決以及無約束非線性優化。讀者將會找到有關激活函數的全球概述、嚴謹的收斂分析，以及對GNN和ZNN動態系統中誤差函數定義的創新改進。

《廣義矩陣逆：機器學習方法》是尋求機器學習、優化和矩陣計算交集的先進方法的研究人員和實踐者的重要資源。

作者簡介

Predrag S. Stanimirovic received his Ph.D. in Computer Science at University of Nis, Serbia. He is full Professor at University of Nis, Faculty of Sciences and Mathematics, Department of Computer Science, Nis, Serbia. He has 36 years of experience in scientific research in diverse fields of mathematics and computer science, spanning multiple branches of numerical linear algebra, recurrent neural networks, linear algebra, nonlinear optimization, symbolic computation and others. His main research topics include Numerical Linear Algebra, Operations Research, Recurrent Neural Networks and Symbolic Computation. He has published over 350 publications in scientific journals, including 7 research monographs, 6 text-books, and over 80 peer-reviewed research articles published in conference proceedings and book chapters. He is an editorial board member of more than 20 scientific journals, 5 of which belong to Journal Citation Report (JCR) list. Currently he is section editor of the journals Electronic Research Archive (ERA), Filomat, Journal of Mathematics, Contemporary Mathematics (CM), Facta Universitatis, Series: Mathematics and Informatics, and several other journals. He is an author in the World Rank List of 2% best authors in 2021, 2022 and 2023.

Yimin Wei received his Ph.D in Computational Mathematics at Fudan University. He is a full Professor with the School of Mathematical Sciences, Fudan University. He is the author of more than 200 technical journal articles and five monographs published by Elsevier, Springer, World Scientific, EDP Science, and Science Press. His current research interests include multilinear algebra and numerical linear algebra with their applications. He is an author in the World's Top 2% Scientists in 2021, 2022 and 2023

Shuai Li received the M.E. degree in automatic control engineering from University of Science and Technology of China, China, and a Ph.D. degree in Electrical and Computer Engineering from Stevens Institute of Technology, Hoboken, NJ, USA in 2014. He is currently a full professor with Faculty of Information Technology and Electrical Engineering, University of Oulu, Finland and an adjunct professor with VTT (Technical Research Center of Finland), Oulu, Finland. His current research interests include dynamic neural networks, robotics, machine learning, and autonomous systems.

Dimitrios K. Gerontitis received a B.S. degree in Mathematics and the M.S. degree in Theoretical Informatics and Systems and Control Theory from the Aristotle University of Thessaloniki, Thessaloniki, Greece, in 2013 and 2016, respectively. He is currently pursuing a Ph.D. degree in the development of intelligent computational methods for solving time-varying problems at the Department of Information and Electronic Engineering, International Hellenic University (IHU). His main research interests include neural networks, optimization methods, robotics, and numerical linear algebra.

Xinwei Cao is a full professor at the School of Business, Jiangnan University, China, with a distinguished interdisciplinary background in both management and computing. She earned her PhD through a joint program between the School of Management at Fudan University and the School of Business at the Chinese University of Hong Kong. Over the years, Dr. Cao has actively collaborated with experts in computing and artificial intelligence to seamlessly integrate AI into management practices. Dr. Cao has published over 50 peer-reviewed scientific papers, reflecting her significant contributions to academia. In addition to her academic work she serves as a consultant and an independent director on audit committees for listed companies.

作者簡介(中文翻譯)

Predrag S. Stanimirovic 於塞爾維亞尼什大學獲得計算機科學博士學位。他是尼什大學科學與數學學院計算機科學系的全職教授。他在數學和計算機科學的多個領域擁有36年的科學研究經驗，涵蓋數值線性代數、遞迴神經網絡、線性代數、非線性優化、符號計算等多個分支。他的主要研究主題包括數值線性代數、運籌學、遞迴神經網絡和符號計算。他在科學期刊上發表了超過350篇出版物，包括7部研究專著、6本教科書，以及超過80篇在會議論文集和書籍章節中發表的同行評審研究文章。他是20多本科學期刊的編輯委員會成員，其中5本屬於期刊引證報告（JCR）名單。目前，他是電子研究檔案（ERA）、Filomat、數學期刊、當代數學（CM）、Facta Universitatis, Series: Mathematics and Informatics等期刊的區域編輯，以及其他幾本期刊的編輯。他在2021年、2022年和2023年被列入全球前2%最佳作者的世界排名名單。

Yimin Wei 於復旦大學獲得計算數學博士學位。他是復旦大學數學科學學院的全職教授。他是超過200篇技術期刊文章和五部由Elsevier、Springer、World Scientific、EDP Science和科學出版社出版的專著的作者。他目前的研究興趣包括多線性代數和數值線性代數及其應用。他在2021年、2022年和2023年被列入全球前2%科學家的名單。

Shuai Li 於2014年獲得中國科學技術大學自動控制工程碩士學位，並在美國新澤西州霍博肯的史蒂文斯理工學院獲得電氣與計算機工程博士學位。他目前是芬蘭奧盧大學資訊技術與電氣工程學院的全職教授，並擔任芬蘭技術研究中心（VTT）的兼任教授。他目前的研究興趣包括動態神經網絡、機器人技術、機器學習和自主系統。

Dimitrios K. Gerontitis 於2013年和2016年分別在希臘塞薩洛尼基的亞里士多德大學獲得數學學士學位和理論資訊學及控制理論碩士學位。他目前在國際希臘大學（IHU）資訊與電子工程系攻讀博士學位，研究主題為解決時間變化問題的智能計算方法的開發。他的主要研究興趣包括神經網絡、優化方法、機器人技術和數值線性代數。

Xinwei Cao 是中國江南大學商學院的全職教授，擁有管理和計算領域的卓越跨學科背景。她通過復旦大學管理學院和香港中文大學商學院的聯合項目獲得博士學位。多年來，Cao博士積極與計算和人工智慧領域的專家合作，將AI無縫整合到管理實踐中。Cao博士已發表超過50篇同行評審的科學論文，反映了她對學術界的重大貢獻。除了學術工作外，她還擔任上市公司的顧問和獨立董事，參與審計委員會。

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