Описание: In a book that will appeal to beginners and experts alike, Oxford University’s Nick Trefethen presents approximation theory using a fresh approach for this established field.Approximation Theory and Approximation Practice is a textbook on classical polynomial and rational approximation theory for the twenty-first century. It uses MATLAB? to teach the field’s most important ideas and results and differs fundamentally from other works on approximation theory in a number of ways: its emphasis is on topics close to numerical algorithms; concepts are illustrated with Chebfun; and each chapter is a PUBLISHable Matlab M-file, available online.In addition, the book centers on theorems and methods for analytic functions, which appear so often in applications, rather than on functions at the edge of discontinuity with their seductive theoretical challenges. Original sources are cited rather than textbooks, and each item in the bibliography is accompanied by an editorial comment.Each chapter has a collection of exercises, which span a wide range from mathematical theory to Chebfun-based numerical experimentation.
Описание: Contains 10 mathematical essays on approximation in Analysis and Topology. This book covers a range of topics, from the intra-history of the involved mathematics to the developments in Differential Equations, Inverse Problems, Analysis, Nonlinear Analysis and Topology. It contains some of the findings concerning the maximum principle.
Автор: Christensen Название: Approximation Theory ISBN: 0817636005 ISBN-13(EAN): 9780817636005 Издательство: Springer Рейтинг: Цена: 5224 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Gives an elementary introduction to approximation theory. This work demonstrates the dynamic nature of mathematics and the influence of classical disciplines on many areas of modern mathematics and applications. It is useful for students and instructors in pure and applied mathematics, mathematical physics, and engineering.
Описание: Entropy quantities are connected with the `degree of compactness` of compact or precompact spaces, and so are appropriate tools for investigating linear and compact operators between Banach spaces.
Описание: Deals with the numerical approximation of partial differential equations. This work provides an illustration of numerical methods, carries out their stability and convergence analysis, derives error bounds, and discusses the algorithmic aspects relative to their implementation.
Автор: DeVore Название: Constructive Approximation ISBN: 3540506276 ISBN-13(EAN): 9783540506270 Издательство: Springer Рейтинг: Цена: 12539 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The purpose of this text is to provide a unified exposition of approximation theory for functions of one real variable. It develops the basic properties of polynomials, splines and linear operators, emphasizing the logical selection of material and the avoidance of superfluous details.
Описание: Presents the basics of classical Fourier Analysis as well as those of approximation by polynomials, splines and entire functions of exponential type. This work includes theorems on convergence. It discusses basic properties of simple and multiple Fourier series.
Описание: This work is devoted to the theory and approximation of nonlinear hyperbolic systems of conservation laws in one or two spaces variables. It concentrates on the systems and theoretical aspects which are needed in the applications, such as the solution of the Riemann problem.
Автор: R. Wong Название: Asymptotic Approximation of Integrals ISBN: 0898714974 ISBN-13(EAN): 9780898714975 Издательство: Eurospan Рейтинг: Цена: 12884 р. Наличие на складе: Поставка под заказ.
Описание: Asymptotic methods are frequently used in many branches of both pure and applied mathematics, and this classic text remains the most up-to-date book dealing with one important aspect of this area, namely, asymptotic approximations of integrals. In this book, all results are proved rigorously, and many of the approximation formulas are accompanied by error bounds. A thorough discussion on multidimensional integrals is given, with references provided. Asymptotic Approximations of Integrals contains the ‘distributional method’, not available elsewhere. Most of the examples in this text come from concrete applications. Since its publication twelve years ago, significant developments have occurred in the general theory of asymptotic expansions, including smoothing of the Stokes phenomenon, uniform exponentially improved asymptotic expansions, and hyperasymptotics. These new concepts belong to the area now known as ‘exponential asymptotics’. Expositions of these new theories are available in papers published in various journals, but not yet in book form.
Автор: Yann Bugeaud Название: Approximation by Algebraic Numbers ISBN: 0521045673 ISBN-13(EAN): 9780521045674 Издательство: Cambridge Academ Рейтинг: Цена: 7476 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Algebraic numbers can approximate and classify any real number. Here, the author gathers together results about such approximations and classifications. Written for a broad audience, the book is accessible and self-contained, with complete and detailed proofs. Starting from continued fractions and Khintchine’s theorem, Bugeaud introduces a variety of techniques, ranging from explicit constructions to metric number theory, including the theory of Hausdorff dimension. So armed, the reader is led to such celebrated advanced results as the proof of Mahler’s conjecture on S-numbers, the Jarnik–Besicovitch theorem, and the existence of T-numbers. Brief consideration is given both to the p-adic and the formal power series cases. Thus the book can be used for graduate courses on Diophantine approximation (some 40 exercises are supplied), or as an introduction for non-experts. Specialists will appreciate the collection of over 50 open problems and the rich and comprehensive list of more than 600 references.
Автор: Berinde Vasile Название: Iterative Approximation of Fixed Points ISBN: 3540722335 ISBN-13(EAN): 9783540722335 Издательство: Springer Рейтинг: Цена: 5951 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The aim of this monograph is to give a unified introductory treatment of the most important iterative methods for constructing fixed points of nonlinear contractive type mappings. It summarizes the most significant contributions in the area by presenting, for each iterative method considered (Picard iteration, Krasnoselskij iteration, Mann iteration, Ishikawa iteration etc.), some of the most relevant, interesting, representative and actual convergence theorems. Applications to the solution of nonlinear operator equations as well as the appropriate error analysis of the main iterative methods, are also presented. Due to the explosive number of research papers on the topic (in the last 15 years only, more than one thousand articles related to the subject were published), it was felt that such a monograph was imperatively necessary. The volume is useful for authors, editors, and reviewers. It introduces concrete criteria for evaluating and judging the plethora of published papers.
Описание: Approximation methods are vital in many challenging applications of computational science and engineering.This is a collection of papers from world experts in a broad variety of relevant applications, including pattern recognition, machine learning, multiscale modelling of fluid flow, metrology, geometric modelling, tomography, signal and image processing.It documents recent theoretical developments which have lead to new trends in approximation, it gives important computational aspects and multidisciplinary applications, thus making it a perfect fit for graduate students and researchers in science and engineering who wish to understand and develop numerical algorithms for the solution of their specific problems.An important feature of the book is that it brings together modern methods from statistics, mathematical modelling and numerical simulation for the solution of relevant problems, with a wide range of inherent scales.Contributions of industrial mathematicians, including representatives from Microsoft and Schlumberger, foster the transfer of the latest approximation methods to real-world applications.
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