Numerical Linear Algebra and Matrix Factorizations
暫譯: 數值線性代數與矩陣分解

Lyche, Tom

Numerical Linear Algebra and Matrix Factorizations
  • 出版商: Springer
  • 出版日期: 2021-03-03
  • 售價: $2,410
  • 貴賓價: 9.5 折 $2,290
  • 語言: 英文
  • 頁數: 371
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 3030364704
  • ISBN-13: 9783030364700
  • 相關分類: 線性代數 Linear-algebra

    • 海外代購書籍(需單獨結帳)

商品描述

After reading this book, students should be able to analyze computational problems in linear algebra such as linear systems, least squares- and eigenvalue problems, and to develop their own algorithms for solving them.

Since these problems can be large and difficult to handle, much can be gained by understanding and taking advantage of special structures. This in turn requires a good grasp of basic numerical linear algebra and matrix factorizations. Factoring a matrix into a product of simpler matrices is a crucial tool in numerical linear algebra, because it allows us to tackle complex problems by solving a sequence of easier ones.

 

The main characteristics of this book are as follows:

It is self-contained, only assuming that readers have completed first-year calculus and an introductory course on linear algebra, and that they have some experience with solving mathematical problems on a computer. The book provides detailed proofs of virtually all results. Further, its respective parts can be used independently, making it suitable for self-study.

The book consists of 15 chapters, divided into five thematically oriented parts. The chapters are designed for a one-week-per-chapter, one-semester course. To facilitate self-study, an introductory chapter includes a brief review of linear algebra.

 

商品描述(中文翻譯)

在閱讀完本書後，學生應能夠分析線性代數中的計算問題，例如線性系統、最小二乘法問題和特徵值問題，並能夠開發自己的算法來解決這些問題。

由於這些問題可能很大且難以處理，因此理解並利用特殊結構可以獲得很大的收益。這反過來又需要對基本的數值線性代數和矩陣分解有良好的掌握。將矩陣分解為簡單矩陣的乘積是數值線性代數中的一個關鍵工具，因為它使我們能夠通過解決一系列較簡單的問題來處理複雜的問題。

本書的主要特點如下：

本書是自成一體的，只假設讀者已完成第一年的微積分和線性代數入門課程，並且有一些在計算機上解決數學問題的經驗。本書提供幾乎所有結果的詳細證明。此外，各部分可以獨立使用，使其適合自學。

本書由15章組成，分為五個主題導向的部分。這些章節設計為每章一週、一學期的課程。為了方便自學，導論章節包括對線性代數的簡要回顧。

作者簡介

The author has a long experience at the university level, teaching numerical analysis, numerical linear algebra and matrix theory, mathematical optimization, approximation theory, and computer aided geometric design.
He has received the Dagstuhl foundation's John Gregory Memorial Award for "Outstanding contributions to geometric modeling" and is a member of Norwegian Academy of Science and Letters.
He has published more than 90 papers in leading international journals and refereed proceedings, edited 17 books and is on the editorial board of 4 international journals. Jointly with Prof. Jean-Louis Merrien, he has published the book "Exercises in Computational Mathematics with MATLAB " published by Springer in 2014.

作者簡介(中文翻譯)

作者在大學層級擁有豐富的教學經驗，教授數值分析、數值線性代數與矩陣理論、數學優化、逼近理論以及計算機輔助幾何設計。

他獲得了Dagstuhl基金會的約翰·格雷戈里紀念獎，以表彰其對「幾何建模的卓越貢獻」，並且是挪威科學與文學學院的成員。

他在國際知名期刊和經過審核的會議論文集中發表了超過90篇論文，編輯了17本書籍，並擔任4本國際期刊的編輯委員會成員。與Jean-Louis Merrien教授共同出版了《使用MATLAB的計算數學習題》（Exercises in Computational Mathematics with MATLAB），該書於2014年由Springer出版。

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