Concise Guide to Numerical Algorithmics: The Foundations and Spirit of Scientific Computing
暫譯: 數值演算法簡明指南:科學計算的基礎與精神

Nazareth, John Lawrence

  • 出版商: Springer
  • 出版日期: 2023-01-03
  • 售價: $2,420
  • 貴賓價: 9.5$2,299
  • 語言: 英文
  • 頁數: 69
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 3031217616
  • ISBN-13: 9783031217616
  • 相關分類: Algorithms-data-structures
  • 海外代購書籍(需單獨結帳)

商品描述

Numerical Algorithmic Science and Engineering (NAS&E), or more compactly, Numerical Algorithmics, is the theoretical and empirical study and the practical implementation and application of algorithms for solving finite-dimensional problems of a numeric nature. The variables of such problems are either discrete-valued, or continuous over the reals, or, and as is often the case, a combination of the two, and they may or may not have an underlying network/graph structure. This re-emerging discipline of numerical algorithmics within computer science is the counterpart of the now well-established discipline of numerical analysis within mathematics, where the latter's emphasis is on infinite-dimensional, continuous numerical problems and their finite-dimensional, continuous approximates.

A discussion of the underlying rationale for numerical algorithmics, its foundational models of computation, its organizational details, and its role, in conjunction with numerical analysis, in support of the modern modus operandi of scientific computing, or computational science & engineering, is the primary focus of this short monograph. It comprises six chapters, each with its own bibliography. Chapters 2, 3 and 6 present the book's primary content. Chapters 1, 4, and 5 are briefer, and they provide contextual material for the three primary chapters and smooth the transition between them. Mathematical formalism has been kept to a minimum, and, whenever possible, visual and verbal forms of presentation are employed and the discussion enlivened through the use of motivating quotations and illustrative examples.

The reader is expected to have a working knowledge of the basics of computer science, an exposure to basic linear algebra and calculus (and perhaps some real analysis), and an understanding of elementary mathematical concepts such as convexity of sets and functions, networks and graphs, and so on. Although this book is not suitable for use as the principal textbook for a course on numerical algorithmics (NAS&E), it will be of value as a supplementary reference for a variety of courses. It can also serve as the primary text for a research seminar. And it can be recommended for self-study of the foundations and organization of NAS&E to graduate and advanced undergraduate students with sufficient mathematical maturity and a background in computing.

When departments of computer science were first created within universities worldwide during the middle of the twentieth century, numerical analysis was an important part of the curriculum. Its role within the discipline of computer science has greatly diminished over time, if not vanished altogether, and specialists in that area are now to be found mainly within other fields, in particular, mathematics and the physical sciences. A central concern of this monograph is the regrettable, downward trajectory of numerical analysis within computer science and how it can be arrested and suitably reconstituted. Resorting to a biblical metaphor, numerical algorithmics (NAS&E) as envisioned herein is neither old wine in new bottles, nor new wine in old bottles, but rather this re-emerging discipline is a decantation of an age-old vintage that can hopefully find its proper place within the larger arena of computer science, and at what appears now to be an opportune time.

商品描述(中文翻譯)

數值演算法科學與工程(Numerical Algorithmic Science and Engineering,簡稱 NAS&E),或更簡潔地稱為數值演算法(Numerical Algorithmics),是對於解決數值性質的有限維問題的演算法進行理論與實證研究,以及實際實施與應用。這類問題的變數可以是離散值(discrete-valued),或在實數上連續(continuous over the reals),或者,通常情況下,兩者的組合,並且它們可能具有或不具有潛在的網路/圖形結構。這一重新興起的數值演算法學科在計算機科學中,是數學中已經建立的數值分析學科的對應物,後者的重點在於無限維的連續數值問題及其有限維的連續近似。

本短篇專著的主要焦點是討論數值演算法的基本原理、其計算模型、組織細節,以及它與數值分析共同支持現代科學計算或計算科學與工程的運作方式。該專著包含六個章節,每個章節都有其自己的參考文獻。第二、第三和第六章呈現本書的主要內容。第一、第四和第五章則較為簡短,提供三個主要章節的背景材料,並平滑它們之間的過渡。數學形式主義被保持在最低限度,並且在可能的情況下,使用視覺和口頭的呈現形式,並通過激勵性的引用和示例來活化討論。

讀者預期具備計算機科學基礎的工作知識,接觸過基本的線性代數和微積分(或許還有一些實分析),並理解基本的數學概念,如集合和函數的凸性、網路和圖形等。雖然本書不適合作為數值演算法(NAS&E)課程的主要教科書,但作為各種課程的補充參考將具有價值。它也可以作為研究研討會的主要文本,並且可以推薦給具有足夠數學成熟度和計算背景的研究生及高年級本科生,自學數值演算法的基礎和組織。

當計算機科學系在二十世紀中期首次在全球大學中成立時,數值分析是課程的重要組成部分。隨著時間的推移,其在計算機科學學科中的角色大幅減少,甚至幾乎消失,該領域的專家現在主要分布在其他領域,特別是數學和物理科學。本專著的一個核心關注點是數值分析在計算機科學中的可惜下滑趨勢,以及如何阻止這一趨勢並適當地重建。借用聖經的隱喻,這裡所構想的數值演算法(NAS&E)既不是舊酒裝在新瓶中,也不是新酒裝在舊瓶中,而是這一重新興起的學科是一種「古老佳釀的倒出」,希望能在計算機科學的更大舞台上找到其適當的位置,而現在似乎正是個合適的時機。