Quantitative Approximation
Quantitative Approximation

Author: Ronald A. Devore

Publisher: Academic Press

Published: 2014-05-10

Total Pages: 337

ISBN-13: 1483265129

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Quantitative Approximation provides information pertinent to nonlinear approximation, including rational approximation and optimal knot spline approximation. This book discusses spline approximation with the most emphasis on multivariate and knot independent questions. Organized into 26 chapters, this book begins with an overview of the inequality for the sharp function in terms of the maximal rearrangement. This text then examines the best co-approximation in a Hilbert space wherein the existence ad uniqueness sets are the closed flats. Other chapters consider the inverse of the coefficient matrix for the system satisfied by the B-spline coefficients of the cubic spline interpolant at knots. This book discusses as well the relationship between the structural properties of a function and its degree of approximation by rational functions. The final chapter deals with the problem of existence of continuous selections for metric projections and provides a solution for this problem. This book is a valuable resource for mathematicians.

Quantitative Approximations
Quantitative Approximations

Author: George Anastassiou

Publisher: CRC Press

Published: 2000-09-15

Total Pages: 626

ISBN-13: 9781584882213

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Quantitative approximation methods apply in many diverse fields of research-neural networks, wavelets, partial differential equations, probability and statistics, functional analysis, and classical analysis to name just a few. For the first time in book form, Quantitative Approximations provides a thorough account of all of the significant developments in the area of contemporary quantitative mathematics. It offers readers the unique opportunity of approaching the field under the guidance of an expert. Among the book's outstanding features is the inclusion of the introductory chapter that summarizes the primary and most useful results. This section serves not only as a more detailed table of contents for those new to an area of application, but also as a quick reference for more seasoned researchers. The author describes all of the pertinent mathematical entities precisely and concretely. His approach and proofs are straightforward and constructive, making Quantitative Approximations accessible and valuable to researchers and graduate students alike.

Quantitative Approximations
Quantitative Approximations

Author: George Anastassiou

Publisher: CRC Press

Published: 2000-09-15

Total Pages: 622

ISBN-13: 1482285797

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Quantitative approximation methods apply in many diverse fields of research-neural networks, wavelets, partial differential equations, probability and statistics, functional analysis, and classical analysis to name just a few. For the first time in book form, Quantitative Approximations provides a thorough account of all of the significant developm

Multivariate Approximation Theory
Multivariate Approximation Theory

Author: E. W. Cheney

Publisher: SIAM

Published: 1986-10-01

Total Pages: 74

ISBN-13: 0898712076

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This monograph deals with the development of algorithms or the derivation of approximations from linear projections.

Rational Approximation of Real Functions
Rational Approximation of Real Functions

Author: P. P. Petrushev

Publisher: Cambridge University Press

Published: 2011-03-03

Total Pages: 388

ISBN-13: 9780521177405

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This 1987 book examines the approximation of real functions by real rational functions. These are a more convenient tool than polynomials, and interest in them was growing, especially after D. Newman's work in the mid-sixties. The authors present the basic achievements of the subject and also discuss some topics from complex rational approximation.

Constructive Approximation
Constructive Approximation

Author: Ronald A. DeVore

Publisher: Springer Science & Business Media

Published: 1993-11-04

Total Pages: 468

ISBN-13: 9783540506270

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Coupled with its sequel, this book gives a connected, unified exposition of Approximation Theory for functions of one real variable. It describes spaces of functions such as Sobolev, Lipschitz, Besov rearrangement-invariant function spaces and interpolation of operators. Other topics include Weierstrauss and best approximation theorems, properties of polynomials and splines. It contains history and proofs with an emphasis on principal results.

Idealization IX: Idealization in Contemporary Physics
Idealization IX: Idealization in Contemporary Physics

Author:

Publisher: BRILL

Published: 2023-05-30

Total Pages: 272

ISBN-13: 9004457631

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Here is presented for the first time a comprehensive review and analysis of the several roles played by idealization procedures in the logic, mathematics and models that lie at the heart of modern, twentieth century physics. It is only through idealization of one form or another that the objects and processes of modern physics become tractable. The essays in this volume will be of interest to all those who are concerned with the uses of models in physics, and the relationships between models and the real world. The essays in this volume cover the role of idealization in all the main areas of modern physics, ranging from quantum theory, relativity theory and cosmology to chaos theory.

n-Widths in Approximation Theory
n-Widths in Approximation Theory

Author: A. Pinkus

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 301

ISBN-13: 3642698948

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My original introduction to this subject was through conservations, and ultimate ly joint work with C. A. Micchelli. I am grateful to him and to Profs. C. de Boor, E. W. Cheney, S. D. Fisher and A. A. Melkman who read various portions of the manuscript and whose suggestions were most helpful. Errors in accuracy and omissions are totally my responsibility. I would like to express my appreciation to the SERC of Great Britain and to the Department of Mathematics of the University of Lancaster for the year spent there during which large portions of the manuscript were written, and also to the European Research Office of the U.S. Army for its financial support of my research endeavors. Thanks are also due to Marion Marks who typed portions of the manuscript. Haifa, 1984 Allan Pinkus Table of Contents 1 Chapter I. Introduction . . . . . . . . Chapter II. Basic Properties of n-Widths . 9 1. Properties of d • • • • • • • • • • 9 n 15 2. Existence of Optimal Subspaces for d • n n 17 3. Properties of d • • • • • • 20 4. Properties of b • • • • • • n 5. Inequalities Between n-Widths 22 n 6. Duality Between d and d • • 27 n 7. n-Widths of Mappings of the Unit Ball 29 8. Some Relationships Between dn(T), dn(T) and bn(T) . 32 37 Notes and References . . . . . . . . . . . . . .

Multiscale, Nonlinear and Adaptive Approximation
Multiscale, Nonlinear and Adaptive Approximation

Author: Ronald DeVore

Publisher: Springer Science & Business Media

Published: 2009-09-16

Total Pages: 671

ISBN-13: 3642034136

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The book of invited articles offers a collection of high-quality papers in selected and highly topical areas of Applied and Numerical Mathematics and Approximation Theory which have some connection to Wolfgang Dahmen's scientific work. On the occasion of his 60th birthday, leading experts have contributed survey and research papers in the areas of Nonlinear Approximation Theory, Numerical Analysis of Partial Differential and Integral Equations, Computer-Aided Geometric Design, and Learning Theory. The main focus and common theme of all the articles in this volume is the mathematics building the foundation for most efficient numerical algorithms for simulating complex phenomena.