Concise Guide to Numerical Algorithmics: The Foundations and Spirit of Scientific Computing

Numerical Algorithmic Science and Engineering (NAS&E) is the theoretical and empirical study and practical implementation and application of algorithms for solving finite-dimensional numeric problems. It is the counterpart of numerical analysis within mathematics, which focuses on infinite-dimensional, continuous numerical problems and their finite-dimensional, continuous approximates. This monograph discusses the underlying rationale for numerical algorithmics, its foundational models of computation, its organizational details, and its role in support of modern scientific computing. It is intended for graduate and advanced undergraduate students with sufficient mathematical maturity and a background in computing.

Format: Paperback / softback
Length: 69 pages
Publication date: 03 January 2023
Publisher: Springer International Publishing AG

Numerical Algorithmic Science and Engineering (NAS&E), also known as Numerical Algorithmics, is a comprehensive field that encompasses the theoretical and empirical exploration, practical implementation, and application of algorithms to solve finite-dimensional problems of a numeric nature. These problems can involve discrete-valued variables, continuous variables over the real numbers, or a combination of both, and may or may not have an underlying network or graph structure. This re-emerging discipline within computer science parallels the well-established field of numerical analysis in mathematics, which focuses on infinite-dimensional and continuous numerical problems and their finite-dimensional and continuous approximations.

The primary objective of this concise monograph is to delve into the underlying rationale, foundational models of computation, organizational structure, and significance of numerical algorithmics in conjunction with numerical analysis in supporting the modern approach to scientific computing, commonly referred to as computational science & engineering. The book is organized into six chapters, each accompanied by a comprehensive bibliography. Chapters 2, 3, and 6 constitute the core content of the book, presenting the main arguments and insights. Chapters 1, 4, and 5 serve as shorter contextual chapters that provide background information, facilitate a smooth transition between the primary chapters, and enhance the overall understanding of the subject matter.

Mathematical formalism has been kept to a minimum throughout the text, with a preference for visual and verbal forms of presentation. Motivating quotations and illustrative examples are incorporated to enliven the discussion and enhance the reader's engagement. It is expected that the reader possesses a foundational understanding of computer science, exposure to basic linear algebra and calculus (and possibly some real analysis), and a willingness to explore the realm of numerical algorithms and their applications.

In conclusion, Numerical Algorithmic Science and Engineering (NAS&E) is a vital and rapidly evolving field that plays a crucial role in solving complex numerical problems across various domains. This monograph provides a comprehensive introduction to the theoretical foundations, practical implementations, and applications of numerical algorithms, offering valuable insights for researchers, practitioners, and students alike.

Weight: 147g
Dimension: 235 x 155 (mm)
ISBN-13: 9783031217616
Edition number: 1st ed. 2023