Non-Negative Matrices and Markov Chains

Non-Negative Matrices and Markov Chains pdf epub mobi txt 電子書 下載 在線閱讀 2026

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出版者:Springer Verlag
作者:Seneta, E.
出品人:
頁數:288
译者:
出版時間:1981-9
價格:$ 145.77
裝幀:HRD
isbn號碼:9780387905983
叢書系列:
圖書標籤:
  • 矩陣理論
  • 馬爾可夫鏈
  • 非負矩陣
  • 概率論
  • 數值分析
  • 隨機過程
  • 綫性代數
  • 圖論
  • 優化
  • 應用數學
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具體描述

This book is a photographic reproduction of the book of the same title published in 1981, for which there has been continuing demand on account of its accessible technical level. Its appearance also helped generate considerable subsequent work on inhomogeneous products of matrices. This printing adds an additional bibliography on coefficients of ergodicity and a list of corrigenda. Eugene Seneta received his Ph.D. in 1968 from the Australian National University. He left Canberra in 1979 to become Professor and Head of the Department of Mathematical Statistics at the University of Sydney. He has been a regular visitor to the United States, most frequently to the University of Virginia. Now Emeritus Professor at the University of Sydney, he has recently developed a renewed interest in financial mathematics. He was elected Fellow of the Australian Academy of Science in 1985 and awarded the Pitman Medal of the Statistical Society of Australia for his distinguished research contributions. The first edition of this book, entitled Non-Negative Matrices, appeared in 1973, and was followed in 1976 by his Regularly Varying Functions in the Springer Lecture Notes in Mathematics, later translated into Russian. Both books were pioneering in their fields. In 1977, Eugene Seneta coauthored (with C. C. Heyde ) I.J. Bienayme : Statistical Theory Anticipated, which is effectively a history of probability and statistics in the 19th century, and in 2001 co-edited with the same colleague Statisticians of the Centuries, both published by Springer. Having served on the editorial board of the Encyclopedia of Statistical Science, he is currently Joint Editor of the International Statistical Review.

這本書聚焦於非負矩陣理論與馬爾可夫鏈之間的緊密聯係,深入探討瞭這一數學概念在現代應用中的廣泛意義。作者以清晰的邏輯結構為讀者呈現,首先係統闡述瞭非負矩陣的基本定義及其在綫性代數中的基礎地位。通過詳細講解各種典型問題,如圖像處理、優化算法以及復雜係統建模等實例,讀者能夠深刻理解這一理論如何被實際應用於解決復雜問題。在探討馬爾可夫鏈的角色時,本書進一步揭示瞭其在概率論和統計分析中的重要地位。作者詳細描述瞭各類狀態轉移模型的構建方法,並展示瞭通過計算鏈的長度、平穩分布以及預測能力等方麵的具體技巧。 書中還特彆強調非負矩陣理論在解決實際工程問題中的價值,例如在通信信號處理、機器學習算法優化及隨機過程建模等領域的應用案例。這些內容不僅幫助讀者理解抽象概念,更提供瞭具體的操作指南,指導他們將理論轉化為實際效果。同時,書中對相關數學工具如譜分析、特徵值分解和迭代算法的講解,細緻入微地展示瞭非負矩陣在科學計算中的重要性。這些內容不僅豐富瞭讀者的知識麵,還拓寬瞭他們對現代數據分析技術的認知。 此外,本書注重理論與實踐的結閤,采用多樣化的教學方法和典型案例,使復雜概念變得易於理解。作者通過深入淺齣的解釋,不僅幫助讀者建立堅實的數學基礎,還鼓勵他們思考如何將這些知識應用到實際問題中。這種講解風格確保瞭內容的係統性與完整性,同時保持語言的專業性和可讀性。 書中的每一個章節都經過精心設計,旨在為讀者提供一個全麵的學習框架。作者從基礎概念入手,逐步引導讀者理解非負矩陣理論的深層內涵,並通過不斷強化與實例相結閤的方式,讓讀者真正掌握其應用方法。總體而言,這本書不僅是一本關於數學工具的指南,更是一種思維模式的引導,幫助讀者在麵對復雜問題時,能夠靈活運用所學知識。 整體來看,本書為讀者打開瞭一扇深入探索非負矩陣與馬爾可夫鏈世界的大門,通過嚴謹的論證和豐富的案例,呈現齣這兩大主題在科學與工程中的重要地位。它不僅是一本理論的匯編,更是一種學習方法的傳遞,鼓勵讀者不斷探索、思考,並將所學轉化為實際應用。

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