B-Series: Algebraic Analysis of Numerical Methods, Butcher John C.
Автор: Burden Annette, Burden Richard, Faires J. Douglas Название: Numerical analysis ISBN: 1305253663 ISBN-13(EAN): 9781305253667 Издательство: Cengage Learning Рейтинг: Цена: 9423.00 р. 13462.00-30% Наличие на складе: Есть (1 шт.) Описание: Introduces readers to the theory and application of modern numerical approximation techniques. Providing an accessible treatment that only requires a calculus prerequisite, the authors explain how, why, and when approximation techniques can be expected to work - and why, in some situations, they fail.
Автор: Bates Название: Numerically Solving Polynomial Systems with Bertini ISBN: 1611972698 ISBN-13(EAN): 9781611972696 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 15107.00 р. Наличие на складе: Нет в наличии.
Описание: This book is a guide to concepts and practice in numerical algebraic geometry - the solution of systems of polynomial equations by numerical methods. Through numerous examples, the authors show how to apply the well-received and widely used open-source Bertini software package to compute solutions, including a detailed manual on syntax and usage options. The authors also maintain a complementary web page where readers can find supplementary materials and Bertini input files.Numerically Solving Polynomial Systems with Bertini approaches numerical algebraic geometry from a user's point of view with numerous examples of how Bertini is applicable to polynomial systems. It treats the fundamental task of solving a given polynomial system and describes the latest advances in the field, including algorithms for intersecting and projecting algebraic sets, methods for treating singular sets, the nascent field of real numerical algebraic geometry, and applications to large polynomial systems arising from differential equations.Those who wish to solve polynomial systems can start gently by finding isolated solutions to small systems, advance rapidly to using algorithms for finding positive-dimensional solution sets (curves, surfaces, etc.), and learn how to use parallel computers on large problems. These techniques are of interest to engineers and scientists in fields where polynomial equations arise, including robotics, control theory, economics, physics, numerical PDEs, and computational chemistry.
Автор: Ming-Jun Lai, Yang Wang Название: Sparse Solutions of Underdetermined Linear Systems ISBN: 1611976502 ISBN-13(EAN): 9781611976502 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 11161.00 р. Наличие на складе: Нет в наличии.
Описание: This textbook presents a special solution of underdetermined linear systems where the number of nonzero entries in the solution is very small compared to the total number of entries. This is called sparse solution. As underdetermined linear systems can be very different, the authors explain how to compute a sparse solution by many approaches.Sparse Solutions of Underdetermined Linear Systems:Contains 72 algorithms for finding sparse solutions of underdetermined linear systems and their applications for matrix completion, graph clustering, and phase retrieval.Provides a detailed explanation of these algorithms including derivations and convergence analysis.Includes exercises for each chapter to help the reader understand the material.This textbook is appropriate for graduate students in math and applied math, computer science, statistics, data science, and engineering. Advisors and postdocs will also find the book of interest.It is appropriate for the following courses: Advanced Numerical Analysis, Special Topics on Numerical Analysis, Topics on Data Science, Topics on Numerical Optimization, and Topics on Approximation Theory.
Автор: Shen Wen Название: Introduction To Numerical Computation, An ISBN: 9814730068 ISBN-13(EAN): 9789814730068 Издательство: World Scientific Publishing Рейтинг: Цена: 8078.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Developed during ten years of teaching experience, this book serves as a set of lecture notes for an introductory course on numerical computation, at the senior undergraduate level.
Автор: Corless Robert Название: Graduate Introduction to Numerical Methods ISBN: 1461484529 ISBN-13(EAN): 9781461484523 Издательство: Springer Рейтинг: Цена: 11179.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book gathers important material from floating-point arithmetic, polynomials, series, interpolation, the discrete Fourier transform, numerical differentiation and integration, numerical solutions of ODEs, BVPs, DDEs, and PDEs, and optimization.
Domain decomposition (DD) methods provide powerful tools for constructing parallel numerical solution algorithms for large scale systems of algebraic equations arising from the discretization of partial differential equations. These methods are well-established and belong to a fast developing area. In this volume, the reader will find a brief historical overview, the basic results of the general theory of domain and space decomposition methods as well as the description and analysis of practical DD algorithms for parallel computing. It is typical to find in this volume that most of the presented DD solvers belong to the family of fast algorithms, where each component is efficient with respect to the arithmetical work. Readers will discover new analysis results for both the well-known basic DD solvers and some DD methods recently devised by the authors, e.g., for elliptic problems with varying chaotically piecewise constant orthotropism without restrictions on the finite aspect ratios.
The hp finite element discretizations, in particular, by spectral elements of elliptic equations are given significant attention in current research and applications. This volume is the first to feature all components of Dirichlet-Dirichlet-type DD solvers for hp discretizations devised as numerical procedures which result in DD solvers that are almost optimal with respect to the computational work. The most important DD solvers are presented in the matrix/vector form algorithms that are convenient for practical use.
Описание: The book presents numerical differential equations to graduate (doctoral) students. It includes the three standard approaches to numerical PDE, FDM, FEM and CM, and the two most common time stepping techniques, FDM and Runge-Kutta. We present both the numerical technique and the supporting mathematical theory.
Автор: Davis Название: Methods of Applied Mathematics with a Software Overview ISBN: 3319433695 ISBN-13(EAN): 9783319433691 Издательство: Springer Рейтинг: Цена: 12577.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This textbook, now in its second edition, provides students with a firm grasp of the fundamental notions and techniques of applied mathematics as well as the software skills to implement them. The text emphasizes the computational aspects of problem solving as well as the limitations and implicit assumptions inherent in the formal methods. Readers are also given a sense of the wide variety of problems in which the presented techniques are useful.Broadly organized around the theme of applied Fourier analysis, the treatment covers classical applications in partial differential equations and boundary value problems, and a substantial number of topics associated with Laplace, Fourier, and discrete transform theories. Some advanced topics are explored in the final chapters such as short-time Fourier analysis and geometrically based transforms applicable to boundary value problems. The topics covered are useful in a variety of applied fields such as continuum mechanics, mathematical physics, control theory, and signal processing.Replete with helpful examples, illustrations, and exercises of varying difficulty, this text can be used for a one- or two-semester course and is ideal for students in pure and applied mathematics, physics, and engineering.Key features of the software overview:Now relies solely on the free software tools Octave, Maxima, and Python.Appendix introduces all of these tools at a level suitable to those with some programming experienceProvides references to sources of further learning.Code snippets incorporated throughout the text. All graphics and illustrations generated using these tools.Praise for the first edition:“The author mixed in a remarkable way theoretical results and applications illustrating the results. Flexibility of presentation (increasing and decreasing level of rigor, accessibility) is a key feature...The book contains extensive examples, presented in an intuitive way with high quality figures (some of them quite spectacular)…” – Mathematica “...Davis's book has many novel features being quite different from most other textbooks on applied mathematics.... Mainly it has a clear and consistent exposition with a strong focus on mathematical fundamentals and useful techniques. It has numerous extensive examples, illustrations, comments, and a very modern graphical presentation of results.“…The book has style. Every theorem and mathematical result has a wonderful appealing comment.” – Studies in Informatics and Control
Описание: A solutions manual to accompany An Introduction toNumerical Methods and Analysis, Second Edition An Introduction to Numerical Methods and Analysis, SecondEdition reflects the latest trends in the field, includesnew material and revised exercises, and offers a unique emphasis onapplications.
Автор: Temme Nico M Название: Asymptotic Methods For Integrals ISBN: 9814612154 ISBN-13(EAN): 9789814612159 Издательство: World Scientific Publishing Рейтинг: Цена: 31680.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
This book gives introductory chapters on the classical basic and standard methods for asymptotic analysis, such as Watson's lemma, Laplace's method, the saddle point and steepest descent methods, stationary phase and Darboux's method. The methods, explained in great detail, will obtain asymptotic approximations of the well-known special functions of mathematical physics and probability theory. After these introductory chapters, the methods of uniform asymptotic analysis are described in which several parameters have influence on typical phenomena: turning points and transition points, coinciding saddle and singularities. In all these examples, the special functions are indicated that describe the peculiar behavior of the integrals.
The text extensively covers the classical methods with an emphasis on how to obtain expansions, and how to use the results for numerical methods, in particular for approximating special functions. In this way, we work with a computational mind: how can we use certain expansions in numerical analysis and in computer programs, how can we compute coefficients, and so on.
Автор: Eilers Название: Introduction to Experimental Mathematics ISBN: 1107156130 ISBN-13(EAN): 9781107156135 Издательство: Cambridge Academ Рейтинг: Цена: 7286.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: A recent surge in computer-based experimental approaches to pure mathematics is revolutionizing the way research mathematicians work. As the first of its kind, this textbook provides students with an introduction to the ends and means of experimental mathematics using the popular computer algebra system Maple.
Описание: Fitted mesh methods focus on the appropriate distribution of the mesh points for singularly perturbed problems. This book offers an introduction to the basic theory associated with fitted numerical methods for singularly perturbed differential equations. It can be used as an introductory text to the theory underpinning fitted mesh methods.
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