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The book "Computational Error and Complexity in Science and Engineering pervades all the science and engineering disciplines where computation occurs. Scientific and engineering computation happens to be the interface between the mathematical model/problem and the real world application. One needs to obtain good quality numerical values for any real-world implementation. Just mathematical quantities symbols are of no use to engineers/technologists. Computational complexity of the numerical method to solve the mathematical model, also computed along with the solution, on the other hand, will tell us how much computation/computational effort has been spent to achieve that quality of result. Anyone who wants the specified physical problem to be solved has every right to know the quality of the solution as well as the resources spent for the solution. The computed error as well as the complexity provide the scientific convincing answer to these questions. Specifically some of the disciplines in which the book will be readily useful are (i) Computational Mathematics, (ii) Applied Mathematics/Computational Engineering, Numerical and Computational Physics, Simulation and Modelling. Operations Research (both deterministic and stochastic), Computing Methodologies, Computer Applications, and Numerical Methods in Engineering.Key Features:- Describes precisely ready-to-use computational error and complexity- Includes simple easy-to-grasp examples wherever necessary.- Presents error and complexity in error-free, parallel, and probabilistic methods.- Discusses deterministic and probabilistic methods with error and complexity. - Points out the scope and limitation of mathematical error-bounds.- Provides a comprehensive up-to-date bibliography after each chapter.· Describes precisely ready-to-use computational error and complexity· Includes simple easy-to-grasp examples wherever necessary.· Presents error and complexity in error-free, parallel, and probabilistic methods.· Discusses deterministic and probabilistic methods with error and complexity. · Points out the scope and limitation of mathematical error-bounds.· Provides a comprehensive up-to-date bibliography after each chapter.
New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.
It is the first text that in addition to standard convergence theory treats other necessary ingredients for successful numerical simulations of physical systems encountered by every practitioner. The book is aimed at users with interests ranging from application modeling to numerical analysis and scientific software development. It is strongly influenced by the authors research in in space physics, electrical and optical engineering, applied mathematics, numerical analysis and professional software development. The material is based on a year-long graduate course taught at the University of Arizona since 1989. The book covers the first two-semesters of a three semester series. The second semester is based on a semester-long project, while the third semester requirement consists of a particular methods course in specific disciplines like computational fluid dynamics, finite element method in mechanical engineering, computational physics, biology, chemistry, photonics, etc.The first three chapters focus on basic properties of partial differential equations, including analysis of the dispersion relation, symmetries, particular solutions and instabilities of the PDEs; methods of discretization and convergence theory for initial value problems. The goal is to progress from observations of simple numerical artifacts like diffusion, damping, dispersion, and anisotropies to their analysis and management technique, as it is not always possible to completely eliminate them.In the second part of the book we cover topics for which there are only sporadic theoretical results, while they are an integral part and often the most important part for successful numerical simulation. We adopt a more heuristic and practical approach using numerical methods of investigation and validation. The aim is teach students subtle key issues in order to separate physics from numerics. The following topics are addressed: Implementation of transparent and absorbing boundary conditions; Practical stability analysis in the presence of the boundaries and interfaces; Treatment of problems with different temporal/spatial scales either explicit or implicit; preservation of symmetries and additional constraints; physical regularization of singularities; resolution enhancement using adaptive mesh refinement and moving meshes. - Self contained presentation of key issues in successful numerical simulation - Accessible to scientists and engineers with diverse background - Provides analysis of the dispersion relation, symmetries, particular solutions and instabilities of the partial differential equations
This book addresses key conceptual issues relating to the modern scientific and engineering use of computer simulations. It analyses a broad set of questions, from the nature of computer simulations to their epistemological power, including the many scientific, social and ethics implications of using computer simulations. The book is written in an easily accessible narrative, one that weaves together philosophical questions and scientific technicalities. It will thus appeal equally to all academic scientists, engineers, and researchers in industry interested in questions (and conceivable answers) related to the general practice of computer simulations.
Our Subjects and Objectives. This book is about algebraic and symbolic computation and numerical computing (with matrices and polynomials). It greatly extends the study of these topics presented in the celebrated books of the seventies, [AHU] and [BM] (these topics have been under-represented in [CLR], which is a highly successful extension and updating of [AHU] otherwise). Compared to [AHU] and [BM] our volume adds extensive material on parallel com putations with general matrices and polynomials, on the bit-complexity of arithmetic computations (including some recent techniques of data compres sion and the study of numerical approximation properties of polynomial and matrix algorithms), and on computations with Toeplitz matrices and other dense structured matrices. The latter subject should attract people working in numerous areas of application (in particular, coding, signal processing, control, algebraic computing and partial differential equations). The au thors' teaching experience at the Graduate Center of the City University of New York and at the University of Pisa suggests that the book may serve as a text for advanced graduate students in mathematics and computer science who have some knowledge of algorithm design and wish to enter the exciting area of algebraic and numerical computing. The potential readership may also include algorithm and software designers and researchers specializing in the design and analysis of algorithms, computational complexity, alge braic and symbolic computing, and numerical computation.
This book commemorates Eric Goles’s achievements in science and engineering. Eric Goles is one of the world leaders in the field of automata and complexity. His groundbreaking discoveries are in the theory and analysis of complex systems, particularly in the field of discrete systems dynamics such as neural networks, automata networks, majority networks, bootstrap percolation models, cellular automata, computational complexity theory, discrete mathematics, and theoretical computer science. Topics include cellular automata, complex networks, models of computation, expansive systems, sandpile automata, Penrose tilings, Boolean automata, models of infection, Fibonacci trees, dominos, reversible automata, and fungal automata. The chapters are authored by world leaders in computer science, physics, mathematics, and engineering. The book will be a pleasure to explore for readers from all walks of life, from undergraduate students to university professors, from mathematicians, computer scientists, and engineers to chemists and biologists.
Classification of articles; Encyclopedia; Appendices.
Zero indicates the absence of a quantity or a magnitude. It is so deeply rooted in our psyche today that nobody will possibly ask "What is zero?" From the beginning of the very creation of life, the feeling of lack of something or the vision of emptiness/void has been embedded by the creator in all living beings. While recognizing different things as well as the absence of one of these things are easy, it is not so easy to fathom the complete nothingness viz. the universal void. Although we have a very good understanding of nothingness or, equivalently, a zero today, our forefathers had devoted countless hours and arrived at the representation and integration of zero and its compatibility not only with all non-zero numbers but also with all conceivable environments only after many painstaking centuries. Zero can be viewed/perceived in two distinct forms: (i) as a number in our mundane affairs and (ii) as the horrific void or Absolute Reality in the spiritual plane/the ultimate state of mind. Presented are the reasons why zero is a landmark discovery and why it has the potential to conjure up in an intense thinker the dreadful nothingness unlike those of other numbers such as 1, 2, and 3. Described are the representation of zero and its history including its deeper understanding via calculus, its occurrences and various roles in different countries as well as in sciences/engineering along with a stress on the Indian zero that is accepted as the time-invariant unique absolute zero. This is followed by the significant distinction between mathematics and computational mathematics and the concerned differences between the unique absolute zero and non-unique relative numerical zeros and their impact and importance in computations on a digital computer. - Introduces the history of the value of zero and why it was a landmark discovery - Discusses how zero is used in science and engineering and its use in different countries - Explains how zero affects different mathematics and calculus
This book differs from traditional numerical analysis texts in that it focuses on the motivation and ideas behind the algorithms presented rather than on detailed analyses of them. It presents a broad overview of methods and software for solving mathematical problems arising in computational modeling and data analysis, including proper problem formulation, selection of effective solution algorithms, and interpretation of results.? In the 20 years since its original publication, the modern, fundamental perspective of this book has aged well, and it continues to be used in the classroom. This Classics edition has been updated to include pointers to Python software and the Chebfun package, expansions on barycentric formulation for Lagrange polynomial interpretation and stochastic methods, and the availability of about 100 interactive educational modules that dynamically illustrate the concepts and algorithms in the book. Scientific Computing: An Introductory Survey, Second Edition is intended as both a textbook and a reference for computationally oriented disciplines that need to solve mathematical problems.
This book constitutes the refereed proceedings of the Third International Conference on Information Computing and Applications, ICICA 2012, held in Chengde, China, in September 2012. The 100 revised full papers were carefully reviewed and selected from 1089 submissions. The papers are organized in topical sections on internet computing and applications, multimedia networking and computing, intelligent computing and applications, computational statistics and applications, cloud and evolutionary computing, computer engineering and applications, knowledge management and applications, communication technology and applications.