Описание: This is a textbook on classical polynomial and rational approximation theory for the twenty-first century. Aimed at advanced undergraduates and graduate students across all of applied mathematics, it uses MATLAB to teach the field’s most important ideas and results.
Approximation Theory and Approximation Practice, Extended Edition 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.
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. In addition, each chapter has a collection of exercises, which span a wide range from mathematical theory to Chebfun-based numerical experimentation.
Автор: Adcock, Ben Brugiapaglia, Simone Webster, Clayton G. Название: Sparse polynomial approximation of high-dimensional functions ISBN: 1611976871 ISBN-13(EAN): 9781611976878 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 10534.00 р. Наличие на складе: Нет в наличии.
Описание: Over seventy years ago, Richard Bellman coined the term "the curse of dimensionality" to describe phenomena and computational challenges that arise in high dimensions. These challenges, in tandem with the ubiquity of high-dimensional functions in real-world applications, have led to a lengthy, focused research effort on high-dimensional approximation—that is, the development of methods for approximating functions of many variables accurately and efficiently from data. This book provides an in-depth treatment of one of the latest installments in this long and ongoing story: sparse polynomial approximation methods. These methods have emerged as useful tools for various high-dimensional approximation tasks arising in a range of applications in computational science and engineering. It begins with a comprehensive overview of best s-term polynomial approximation theory for holomorphic, high-dimensional functions, as well as a detailed survey of applications to parametric differential equations. It then describes methods for computing sparse polynomial approximations, focusing on least squares and compressed sensing techniques.Sparse Polynomial Approximation of High-Dimensional Functions presents the first comprehensive and unified treatment of polynomial approximation techniques that can mitigate the curse of dimensionality in high-dimensional approximation, including least squares and compressed sensing. It develops main concepts in a mathematically rigorous manner, with full proofs given wherever possible, and it contains many numerical examples, each accompanied by downloadable code. The authors provide an extensive bibliography of over 350 relevant references, with an additional annotated bibliography available on the book's companion website (www.sparse-hd-book.com).This text is aimed at graduate students, postdoctoral fellows, and researchers in mathematics, computer science, and engineering who are interested in high-dimensional polynomial approximation techniques.
Описание: This book mainly focuses on MOR techniques for the first and second order descriptor systems. The book also provides mathematical algorithms for implementing them in real-world applications. This book is intended for assisting undergraduates, graduates and researchers in academics and industries.
Автор: L. Ljung; G. Pflug; H. Walk Название: Stochastic Approximation and Optimization of Random Systems ISBN: 3764327332 ISBN-13(EAN): 9783764327330 Издательство: Springer Рейтинг: Цена: 3487.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: PHug) 7 Markovian stochastic optimization and stochastic approximation procedures 53 8 Asymptotic distributions 71 9 Stopping times 79 1O Applications of stochastic approximation methods 80 References for Part II 90 III Applications to adaptation algorithms (L.
Описание: This text presents various new results within the areas covered by the workshop.
Автор: Dung, Dinh Temlyakov, Vladimir Ullrich, Tino Название: Hyperbolic cross approximation ISBN: 3319922394 ISBN-13(EAN): 9783319922393 Издательство: Springer Рейтинг: Цена: 6288.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book provides a systematic survey of classical and recent results on hyperbolic cross approximation. Motivated by numerous applications, the last two decades have seen great success in studying multivariate approximation. Multivariate problems have proven to be considerably more difficult than their univariate counterparts, and recent findings have established that multivariate mixed smoothness classes play a fundamental role in high-dimensional approximation. The book presents essential findings on and discussions of linear and nonlinear approximations of the mixed smoothness classes. Many of the important open problems explored here will provide both students and professionals with inspirations for further research.
Автор: Merlevede, Florence (professor, Universite Paris-est Marne-la-vallee) Peligrad, Magda (professor, University Of Cincinnati) Utev, Sergey (university O Название: Functional gaussian approximation for dependent structures ISBN: 019882694X ISBN-13(EAN): 9780198826941 Издательство: Oxford Academ Рейтинг: Цена: 17820.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book has its origin in the need of developing and analysing mathematical models for phenomena that evolve in time and influence each another, and aims at a better understanding of the structure and asymptotic behaviour of stochastic processes.
Автор: Anastassiou George A Название: Advances in Applied Mathematics and Approximation Theory ISBN: 1461463920 ISBN-13(EAN): 9781461463924 Издательство: Springer Рейтинг: Цена: 16769.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Advances in Applied Mathematics and Approximation Theory: Contributions from AMAT 2012 is a collection of the best articles presented at "Applied Mathematics and Approximation Theory 2012," an international conference held in Ankara, Turkey, May 17-20, 2012.
Автор: Werner Haussmann; Kurt Jetter; Manfred Reimer Название: Recent Progress in Multivariate Approximation ISBN: 3034894988 ISBN-13(EAN): 9783034894982 Издательство: Springer Рейтинг: Цена: 6986.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Nineteen contributions cover recent topics in constructive approximation on varieties, approximation by solutions of partial differential equations, application of Riesz bases and frames, multiwavelets and subdivision.
Автор: George A. Anastassiou; Sorin G. Gal Название: Approximation Theory ISBN: 1461271126 ISBN-13(EAN): 9781461271123 Издательство: Springer Рейтинг: Цена: 13974.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: We study in Part I of this monograph the computational aspect of almost all moduli of continuity over wide classes of functions exploiting some of their convexity properties. To our knowledge it is the first time the entire calculus of moduli of smoothness has been included in a book. We then present numerous applications of Approximation Theory, giving exact val- ues of errors in explicit forms. The K-functional method is systematically avoided since it produces nonexplicit constants. All other related books so far have allocated very little space to the computational aspect of moduli of smoothness. In Part II, we study/examine the Global Smoothness Preservation Prop- erty (GSPP) for almost all known linear approximation operators of ap- proximation theory including: trigonometric operators and algebraic in- terpolation operators of Lagrange, Hermite-Fejer and Shepard type, also operators of stochastic type, convolution type, wavelet type integral opera- tors and singular integral operators, etc. We present also a sufficient general theory for GSPP to hold true. We provide a great variety of applications of GSPP to Approximation Theory and many other fields of mathemat- ics such as Functional analysis, and outside of mathematics, fields such as computer-aided geometric design (CAGD). Most of the time GSPP meth- ods are optimal. Various moduli of smoothness are intensively involved in Part II. Therefore, methods from Part I can be used to calculate exactly the error of global smoothness preservation. It is the first time in the literature that a book has studied GSPP.
Автор: Vladimir V. Andrievskii; Hans-Peter Blatt Название: Discrepancy of Signed Measures and Polynomial Approximation ISBN: 1441931465 ISBN-13(EAN): 9781441931467 Издательство: Springer Рейтинг: Цена: 25853.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: A concise outline of the basic facts of potential theory and quasiconformal mappings makes this book an ideal introduction for non-experts who want to get an idea of applications of potential theory and geometric function theory in various fields of construction analysis.
Автор: Piero Pagliani; Mihir Chakraborty Название: A Geometry of Approximation ISBN: 9048179351 ISBN-13(EAN): 9789048179350 Издательство: Springer Рейтинг: Цена: 48076.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: A Geometry of Approximation addresses Rough Set Theory. It focuses mainly on its logic-algebraic interpretation. The theory is embedded in a broader perspective and this is the first book to place Rough Set Theory in a broad historical and applied setting.
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