Concise Guide To Numerical Algorithmics
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Concise Guide to Numerical Algorithmics
Author: John Lawrence Nazareth
language: en
Publisher: Springer Nature
Release Date: 2023-01-02
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.
Numerical Simulation - Advanced Techniques for Science and Engineering
Author: Ali Soofastaei
language: en
Publisher: BoD – Books on Demand
Release Date: 2023-11-15
Numerical simulation is a powerful tool used in various fields of science and engineering to model complex systems and predict their behavior. It involves developing mathematical models that describe the behavior of a system and using computer algorithms to solve these models numerically. By doing so, researchers and engineers can study the behavior of a system in detail, which may only be possible with analytical methods. Numerical simulation has many advantages over traditional analytical methods. It allows researchers and engineers to study complex systems’ behavior in detail and predict their behavior in different scenarios. It also allows for the optimization of systems and the identification of design flaws before they are built. However, numerical simulation has its limitations. It requires significant computational resources, and the accuracy of the results depends on the quality of the mathematical models and the discretization methods used. Nevertheless, numerical simulation remains a valuable tool in many fields and its importance is likely to grow as computational resources become more powerful and widely available. Numerical simulation is widely used in physics, engineering, computer science, and mathematics. In physics, for example, numerical simulation is used to study the behavior of complex systems such as weather patterns, fluid dynamics, and particle interactions. In engineering, it is used to design and optimize systems such as aircraft, cars, and buildings. In computer science, numerical simulation models and optimization algorithms and data structures. In mathematics, it is used to study complex mathematical models and to solve complex equations. This book familiarizes readers with the practical application of the numerical simulation technique to solve complex analytical problems in different industries and sciences.
Extremal Optimization
Extremal Optimization: Fundamentals, Algorithms, and Applications introduces state-of-the-art extremal optimization (EO) and modified EO (MEO) solutions from fundamentals, methodologies, and algorithms to applications based on numerous classic publications and the authors’ recent original research results. It promotes the movement of EO from academic study to practical applications. The book covers four aspects, beginning with a general review of real-world optimization problems and popular solutions with a focus on computational complexity, such as "NP-hard" and the "phase transitions" occurring on the search landscape. Next, it introduces computational extremal dynamics and its applications in EO from principles, mechanisms, and algorithms to the experiments on some benchmark problems such as TSP, spin glass, Max-SAT (maximum satisfiability), and graph partition. It then presents studies on the fundamental features of search dynamics and mechanisms in EO with a focus on self-organized optimization, evolutionary probability distribution, and structure features (e.g., backbones), which are based on the authors’ recent research results. Finally, it discusses applications of EO and MEO in multiobjective optimization, systems modeling, intelligent control, and production scheduling. The authors present the advanced features of EO in solving NP-hard problems through problem formulation, algorithms, and simulation studies on popular benchmarks and industrial applications. They also focus on the development of MEO and its applications. This book can be used as a reference for graduate students, research developers, and practical engineers who work on developing optimization solutions for those complex systems with hardness that cannot be solved with mathematical optimization or other computational intelligence, such as evolutionary computations.