Numerical Methods for Scientists and Engineers, 2/e (Paperback)

R. W. Hamming

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Numerical analysis is a subject of extreme interest to mathematicians and computer scientists, who will welcome this first inexpensive paperback edition of a groundbreaking classic text on the subject. In an introductory chapter on numerical methods and their relevance to computing, well-known mathematician Richard Hamming ("the Hamming code," "the Hamming distance," and "Hamming window," etc.), suggests that the purpose of computing is insight, not merely numbers. In that connection he outlines five main ideas that aim at producing meaningful numbers that will be read and used, but will also lead to greater understanding of how the choice of a particular formula or algorithm influences not only the computing but our understanding of the results obtained.
The five main ideas involve (1) insuring that in computing there is an intimate connection between the source of the problem and the usability of the answers (2) avoiding isolated formulas and algorithms in favor of a systematic study of alternate ways of doing the problem (3) avoidance of roundoff (4) overcoming the problem of truncation error (5) insuring the stability of a feedback system.
In this second edition, Professor Hamming (Naval Postgraduate School, Monterey, California) extensively rearranged, rewrote and enlarged the material. Moreover, this book is unique in its emphasis on the frequency approach and its use in the solution of problems. Contents include:
I. Fundamentals and Algorithms
II. Polynomial Approximation- Classical Theory
Ill. Fourier Approximation- Modern Theory
IV. Exponential Approximation ... and more
Highly regarded by experts in the field, this is a book with unlimited applications for undergraduate and graduate students of mathematics, science and engineering. Professionals and researchers will find it a valuable reference they will turn to again and again.

商品描述(中文翻譯)

數值分析是數學家和計算機科學家極感興趣的一門學科,他們將歡迎這本關於該主題的開創性經典文本的首個廉價平裝版。在關於數值方法及其與計算的相關性的引言章節中,著名數學家Richard Hamming(“Hamming碼”,“Hamming距離”和“Hamming窗口”等)提出了計算的目的是洞察力,而不僅僅是數字。在這方面,他概述了五個主要想法,旨在產生有意義的數字,這些數字將被閱讀和使用,但也將導致對特定公式或算法的選擇如何影響計算以及我們對所獲結果的理解的更深入了解。

這五個主要想法包括:(1)確保在計算中問題的來源與答案的可用性之間存在密切聯繫;(2)避免孤立的公式和算法,而是系統地研究解決問題的替代方法;(3)避免四捨五入;(4)克服截斷誤差的問題;(5)確保反饋系統的穩定性。

在這第二版中,Hamming教授(加州蒙特雷海軍研究生院)對材料進行了廣泛的重新排列、重寫和擴充。此外,這本書在強調頻率方法及其在解決問題中的應用方面是獨一無二的。內容包括:

I. 基礎和算法
II. 多項式逼近-經典理論
III. 傅立葉逼近-現代理論
IV. 指數逼近...等等

這本書在該領域的專家中享有很高的聲譽,對於數學、科學和工程的本科和研究生學生來說,它具有無限的應用價值。專業人士和研究人員將發現它是一個寶貴的參考資料,他們將一再求助於此書。