Автор: Arora, Sanjeev Barak, Boaz Название: Computational complexity ISBN: 0521424267 ISBN-13(EAN): 9780521424264 Издательство: Cambridge Academ Рейтинг: Цена: 7120 р. Наличие на складе: Поставка под заказ.
Описание: This beginning graduate textbook describes both recent achievements and classical results of computational complexity theory. Requiring essentially no background apart from mathematical maturity, the book can be used as a reference for self-study for anyone interested in complexity, including physicists, mathematicians, and other scientists, as well as a textbook for a variety of courses and seminars. More than 300 exercises are included with a selected hint set. The book starts with a broad introduction to the field and progresses to advanced results. Contents include: definition of Turing machines and basic time and space complexity classes, probabilistic algorithms, interactive proofs, cryptography, quantum computation, lower bounds for concrete computational models (decision trees, communication complexity, constant depth, algebraic and monotone circuits, proof complexity), average-case complexity and hardness amplification, derandomization and pseudorandom constructions, and the PCP theorem.
This book presents the main concepts of linear algebra from the viewpoint of applied scientists such as computer scientists and engineers, without compromising on mathematical rigor. Based on the idea that computational scientists and engineers need, in both research and professional life, an understanding of theoretical concepts of mathematics in order to be able to propose research advances and innovative solutions, every concept is thoroughly introduced and is accompanied by its informal interpretation. Furthermore, most of the theorems included are first rigorously proved and then shown in practice by a numerical example. When appropriate, topics are presented also by means of pseudocodes, thus highlighting the computer implementation of algebraic theory.
It is structured to be accessible to everybody, from students of pure mathematics who are approaching algebra for the first time to researchers and graduate students in applied sciences who need a theoretical manual of algebra to successfully perform their research. Most importantly, this book is designed to be ideal for both theoretical and practical minds and to offer to both alternative and complementary perspectives to study and understand linear algebra.
Описание: The goal of this book is to teach computational scientists how to develop tailored, flexible, and human-efficient working environments built from small programs
(scripts) written in the easy-to-learn, high-level language Python. The focus is on examples and applications of relevance to computational scientists: gluing existing applications and
tools, e.g. for automating simulation, data analysis, and visualization; steering simulations and computational experiments; equipping old programs with graphical user interfaces; making
computational Web applications; and creating interactive interfaces with a Maple/Matlab-like syntax to numerical applications in C/C++ or Fortran.
In short, scripting with
Python makes you much more productive, increases the reliability of your scientific work and lets you have more fun - on Unix, Windows and Macintosh. All the tools and examples in
this book are open source codes. The second edition features new material, reorganization of text, improved examples and tools, updated information, and correction of errors.
Описание: This introductory level text is suitable for use by advanced undergraduate and graduate students of computational biology. Written by experienced authors, it provides detailed coverage of many algorithms, including applications and possible modifications.
Описание: This book describes 148 algorithms which are fundamental for number-theoretic computations, in particular for computations related to algebraic number theory, elliptic curves, primality testing and factoring. The first seven chapters lead the reader to the heart of current research in computational algebraic number theory, including recent algorithms for computing class groups and units, as well as elliptic curve computations. The last three chapters give a survey of factoring and primality testing methods, including a detailed description of the number field sieve algorithm. The book ends with a description of available computer packages and some useful tables. The book also contains a large number of exercises. Written by an authority in the field, and one with great practical and teaching experience it is sure to become the standard and indispensable reference on the subject.
Описание: The book is aimed at graduate students, researchers, engineers and physicists involved in fluid computations. An up-to-date account is given of the present state of the art of numerical methods employed in computational fluid dynamics. The underlying numerical principles are treated with a fair amount of detail, using elementary methods. Attention is given to the difficulties arising from geometric complexity of the flow domain. Uniform accuracy for singular perturbation problems is studied, pointing the way to accurate computation of flows at high Reynolds number. Unified methods for compressible and incompressible flows are discussed. A treatment of the shallow-water equations is included. A basic introduction is given to efficient iterative solution methods. Many pointers are given to the current literature, facilitating further study.
Автор: J.R. Sack Название: Handbook of Computational Geometry, ISBN: 0444825371 ISBN-13(EAN): 9780444825377 Издательство: Elsevier Science Рейтинг: Цена: 27720 р. Наличие на складе: Поставка под заказ.
Описание: Computational Geometry is an area that provides solutions to geometric problems which arise in applications including Geographic Information Systems, Robotics and Computer Graphics. This Handbook provides an overview of key concepts and results in Computational Geometry. It serves as a reference and study guide to the field.
Описание: Spatial statistics and Markov Chain Monte Carlo (MCMC) techniques have each undergone major developments in the last decade. Also, these two areas are mutually reinforcing, because MCMC methods are often necessary for the practical implementation of spatial statistical inference, while new spatial stochastic models in turn motivate the development of improved MCMC algorithms. This volume shows how sophisticated spatial statistical and computational methods apply to a range of problems of increasing importance for applications in science and technology. It consists of four chapters: 1. Petros Dellaportas and Gareth O. Roberts give a tutorial on MCMC methods, the computational methodology which is essential for virtually all the complex spatial models to be considered in subsequent chapters. 2. Peter J. Diggle, Paulo J, Ribeiro Jr., and Ole F. Christensen introduce the reader to the model-based approach to geostatistics, i.e. the application of general statistical principles to the formulation of explicit stochastic models for geostatistical data, and to inference within a declared class of models. 3. Merrilee A. Hurn, Oddvar K. Husby, and HГҐvard Rue discuss various aspects of image analysis, ranging from low to high level tasks, and illustrated with different examples of applications. 4. Jesper Moller and Rasmus P. Waggepetersen collect recent theoretical advances in simulation-based inference for spatial point processes, and discuss some examples of applications. The volume introduces topics of current interest in spatial and computational statistics, which should be accessible to postgraduate students as well as to experienced statistical researchers. It is partly based on the course material for the "TMR and MaPhySto Summer School on Spatial Statistics and Computational Methods," held at Aalborg University, Denmark, August 19-22, 2001. The editor, Jesper Moller, Professor of statistics at Aalborg University, and the above-mentioned contributors have all been associated with the European Union's TMR network "Statistics and Computational Methods for the Analysis of Spatial Data. ERB-FMRX-CT96-0095."
Описание: This book constitutes the thoroughly refereed post-proceedings of the Japanese Conference on Discrete Computational Geometry, JCDCG 2001, held in Tokyo, Japan in November 2001. The 35 revised papers presented were carefully reviewed and selected. Among the topics covered are polygons and polyhedrons, divissible dissections, convex polygon packings, symmetric subsets, convex decompositions, graph drawing, graph computations, point sets, approximation, Delauny diagrams, triangulations, chromatic numbers, complexity, layer routing, efficient algorithms, and illumination problems.
Описание: This tutorial contains written versions of seven lectures on Computational Combinatorial Optimization given by leading members of the optimization community. The lectures introduce modern combinatorial optimization techniques, with an emphasis on branch and cut algorithms and Lagrangian relaxation approaches. Polyhedral combinatorics as the mathematical backbone of successful algorithms are covered from many perspectives, in particular, polyhedral projection and lifting techniques and the importance of modeling are extensively discussed. Applications to prominent combinatorial optimization problems, e.g., in production and transport planning, are treated in many places; in particular, the book contains a state-of-the-art account of the most successful techniques for solving the traveling salesman problem to optimality.
Автор: Derksen Harm, Kemper Gregor Название: Computational Invariant Theory ISBN: 3540434763 ISBN-13(EAN): 9783540434764 Издательство: Springer Рейтинг: Цена: 11198 р. Наличие на складе: Поставка под заказ.
Описание: Throughout the history of invariant theory, computational methods have always been at the center of attention. This book, the first volume of the new subseries on "Invariant Theory and Algebraic Transformation Groups", provides a comprehensive and up-to-date overview of the algorithmic aspects of invariant theory. Special features are an introductory chapter on GrГ¶bner basis methods and a chapter on applications, covering fields as disparate as graph theory, coding theory, dynamical systems, and computer vision. Both authors have made significant contributions to the theory and practice of algorithmic invariant theory. Numerous illustrative examples and a careful selection of proofs make the book accessible to non-specialists.The book will be very useful to postgraduate students as well as researchers in geometry, computer algebra, and, of course, invariant theory.
Описание: In this book, 16 experts describe the application of methods of statistical physics to various areas in physics: disordered materials, quasicrystals, semiconductors, and also to other areas beyond physics, such as financial markets, game theory, evolution, and traffic planning, in which statistical physics has recently become significant.
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