Описание: This book presents a twenty-first century approach to classical polynomial and rational approximation theory. The reader will find a strikingly original treatment of the subject, completely unlike any of the existing literature on approximation theory, with a rich set of both computational and theoretical exercises for the classroom. There are many original features that set this book apart: the emphasis is on topics close to numerical algorithms; every idea is illustrated with Chebfun examples; each chapter has an accompanying Matlab file for the reader to download; the text focuses on theorems and methods for analytic functions; original sources are cited rather than textbooks, and each item in the bibliography is accompanied by an editorial comment. This textbook is ideal for advanced undergraduates and graduate students across all of applied mathematics.
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.
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.
Автор: DeVore Название: Constructive Approximation ISBN: 3540506276 ISBN-13(EAN): 9783540506270 Издательство: Springer Рейтинг: Цена: 12150 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.
Автор: Berinde Vasile Название: Iterative Approximation of Fixed Points ISBN: 3540722335 ISBN-13(EAN): 9783540722335 Издательство: Springer Рейтинг: Цена: 5325 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: Model reduction is an important engineering problem in which one aims to replace an elaborate model by a simpler model without undue loss of accuracy. The accuracy can be mathematically measured in several possible norms and the Hankel norm is one such. The Hankel norm gives a meaningful notion of distance between two linear systems: roughly speaking, it is the induced norm of the operator that maps past inputs to future outputs. It turns out that the engineering problem of model reduction in the Hankel norm is closely related to the mathematical problem of finding solutions to the sub-optimal Nehari-Takagi problem, which is called "the sub-optimal Hankel norm approximation problem" in this book. Although the existence of a solution to the sub-optimal Hankel norm approximation problem has been known since the 1970's, this book presents explicit solutions and, in particular, new formulae for several large classes of infinite-dimensional systems for the first time.
Автор: R. Wong Название: Asymptotic Approximation of Integrals ISBN: 0898714974 ISBN-13(EAN): 9780898714975 Издательство: Cambridge Academ Рейтинг: Цена: 6349 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: 4787 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: Deutsch Frank R. Название: Best Approximation in Inner Product Spaces ISBN: 0387951563 ISBN-13(EAN): 9780387951560 Издательство: Springer Рейтинг: Цена: 7008 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This is the first systematic study of best approximation theory in inner product spaces and, in particular, in Hilbert space. Geometric considerations play a prominent role in developing and understanding the theory. The only prerequisite for reading the book is some knowledge of advanced calculus and linear algebra. Throughout the book, examples and applications have been interspersed with the theory. Each chapter concludes with numerous exercises and a section in which the author puts the results of that chapter into a historical perspective. The book is based on lecture notes for a graduate course on best approximation which the author has taught for over 25 years.
Описание: Classical boundary integral equations arising from the potential theory and acoustics (Laplace and Helmholtz equations) are derived. Using the parametrization of the boundary these equations take a form of periodic pseudodifferential equations. A general theory of periodic pseudodifferential equations and methods of solving are developed, including trigonometric Galerkin and collocation methods, their fully discrete versions with fast solvers, quadrature and spline based methods. The theory of periodic pseudodifferential operators is presented in details, with preliminaries (Fredholm operators, periodic distributions, periodic Sobolev spaces) and full proofs. This self-contained monograph can be used as a textbook by graduate/postgraduate students. It also contains a lot of carefully chosen exercises.
Автор: Christensen Название: Approximation Theory ISBN: 0817636005 ISBN-13(EAN): 9780817636005 Издательство: Springer Рейтинг: Цена: 2804 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.
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