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Author: G. G. Lorentz
Publisher: American Mathematical Soc.
ISBN: 0821875582
Category : Mathematics
Languages : en
Pages : 146
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Book Description
Bernstein polynomials are a remarkable family of polynomials associated to any given function on the unit interval. Their first notable appearance was in Bernstein's proof of the Weierstrass approximation theorem. This book gives an exhaustive exposition of the main facts about the Bernstein polynomials and discusses some of their applications in analysis. The first three chapters of the book give an introduction to a theory of singular integrals by means of the particular instance of Bernstein polynomials. The author writes in the preface to this second edition, "After the trigonometric integrals, Bernstein polynomials are the most important and interesting concrete operators on a space of continuous functions. Since the appearance of the first edition of this book [in 1953], the interest in this subject has continued. In an appendix we have summed up a few of the most important papers that have appeared since."
Author: G. G. Lorentz
Publisher: American Mathematical Soc.
ISBN: 0821875582
Category : Mathematics
Languages : en
Pages : 146
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Book Description
Bernstein polynomials are a remarkable family of polynomials associated to any given function on the unit interval. Their first notable appearance was in Bernstein's proof of the Weierstrass approximation theorem. This book gives an exhaustive exposition of the main facts about the Bernstein polynomials and discusses some of their applications in analysis. The first three chapters of the book give an introduction to a theory of singular integrals by means of the particular instance of Bernstein polynomials. The author writes in the preface to this second edition, "After the trigonometric integrals, Bernstein polynomials are the most important and interesting concrete operators on a space of continuous functions. Since the appearance of the first edition of this book [in 1953], the interest in this subject has continued. In an appendix we have summed up a few of the most important papers that have appeared since."
Author: George M. Phillips
Publisher: Springer Science & Business Media
ISBN: 0387216820
Category : Mathematics
Languages : en
Pages : 325
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Book Description
In addition to coverage of univariate interpolation and approximation, the text includes material on multivariate interpolation and multivariate numerical integration, a generalization of the Bernstein polynomials that has not previously appeared in book form, and a greater coverage of Peano kernel theory than is found in most textbooks. There are many worked examples and each section ends with a number of carefully selected problems that extend the student's understanding of the text. The author is well known for his clarity of writing and his many contributions as a researcher in approximation theory.
Author: Ming-Jun Lai
Publisher: Cambridge University Press
ISBN: 0521875927
Category : Mathematics
Languages : en
Pages : 28
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Book Description
Comprehensive graduate text offering a detailed mathematical treatment of polynomial splines on triangulations.
Author: Robert B. Gardner
Publisher: Elsevier
ISBN: 0128119888
Category : Mathematics
Languages : en
Pages : 442
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Book Description
Bernstein-type Inequalities for Polynomials and Rational Functions is an integrated, powerful and clear presentation of the emergent field in approximation theory. It presents a unified description of solution norms relevant to complex polynomials, rational functions and exponential functions. Primarily for graduate students and first year PhDs, this book is useful for any researcher exploring problems which require derivative estimates. It is particularly useful for those studying inverse problems in approximation theory. Applies Bernstein-type Inequalities to any problem where derivative estimates are necessary Presents complex math in a clean and simple way, progressing readers from polynomials into rational functions Contains exhaustive references with thousands of citations to articles and books Features methods to solve inverse problems across approximation theory Includes open problems for further research
Author: Jorge Bustamante
Publisher: Birkhäuser
ISBN: 3319554026
Category : Mathematics
Languages : en
Pages : 423
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Book Description
This book provides comprehensive information on the main aspects of Bernstein operators, based on the literature to date. Bernstein operators have a long-standing history and many papers have been written on them. Among all types of positive linear operators, they occupy a unique position because of their elegance and notable approximation properties. This book presents carefully selected material from the vast body of literature on this topic. In addition, it highlights new material, including several results (with proofs) appearing in a book for the first time. To facilitate comprehension, exercises are included at the end of each chapter. The book is largely self-contained and the methods in the proofs are kept as straightforward as possible. Further, it requires only a basic grasp of analysis, making it a valuable and appealing resource for advanced graduate students and researchers alike.
Author: Kenneth L. Judd
Publisher: MIT Press
ISBN: 9780262100717
Category : Business & Economics
Languages : en
Pages : 662
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Book Description
To harness the full power of computer technology, economists need to use a broad range of mathematical techniques. In this book, Kenneth Judd presents techniques from the numerical analysis and applied mathematics literatures and shows how to use them in economic analyses. The book is divided into five parts. Part I provides a general introduction. Part II presents basics from numerical analysis on R^n, including linear equations, iterative methods, optimization, nonlinear equations, approximation methods, numerical integration and differentiation, and Monte Carlo methods. Part III covers methods for dynamic problems, including finite difference methods, projection methods, and numerical dynamic programming. Part IV covers perturbation and asymptotic solution methods. Finally, Part V covers applications to dynamic equilibrium analysis, including solution methods for perfect foresight models and rational expectation models. A website contains supplementary material including programs and answers to exercises.
Author: Sorin G. Gal
Publisher: Springer Science & Business Media
ISBN: 0817647031
Category : Mathematics
Languages : en
Pages : 359
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Book Description
First comprehensive treatment in book form of shape-preserving approximation by real or complex polynomials in one or several variables Of interest to grad students and researchers in approximation theory, mathematical analysis, numerical analysis, Computer Aided Geometric Design, robotics, data fitting, chemistry, fluid mechanics, and engineering Contains many open problems to spur future research Rich and updated bibliography
Author: Gengzhe Chang
Publisher: Cambridge University Press
ISBN: 9780883856413
Category : Mathematics
Languages : en
Pages : 328
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Book Description
Mathematical theme that relates chaos, graphics and geometry, all with just high school maths background.
Author: Frank Klawonn
Publisher: Springer Science & Business Media
ISBN: 1846288487
Category : Computers
Languages : en
Pages : 296
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Book Description
This book provides an introduction to the most important basic concepts of computer graphics. It couples the technical background and theory immediately with practical examples and applications. The reader can follow up the theory and then literally see the theory at work in numerous example programs. With only elementary knowledge of the programming language Java, the reader will be able to create his or her own images and animations immediately using Java 2D and Java 3D. A website for this book includes programs with source code, exercises with solutions and slides as teaching material.
Author: Ronald A. DeVore
Publisher: Springer Science & Business Media
ISBN: 9783540506270
Category : Mathematics
Languages : en
Pages : 468
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Book Description
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.
