Approximation Theory and Approximation Practice

Author: Lloyd N. Trefethen

Publisher: SIAM

ISBN: 9781611972405

Category: Mathematics

Page: 295

View: 8695

An original and modern treatment of approximation theory for students in applied mathematics. Includes exercises, illustrations and Matlab code.

Approximation Theory and Approximation Practice

Author: Lloyd N. Trefethen

Publisher: SIAM

ISBN: 1611972396

Category: Mathematics

Page: 295

View: 4841

An original and modern treatment of approximation theory for students in applied mathematics. Includes exercises, illustrations and Matlab code.

Approximation Theory and Methods

Author: M. J. D. Powell

Publisher: Cambridge University Press

ISBN: 9780521295147

Category: Mathematics

Page: 339

View: 5128

Most functions that occur in mathematics cannot be used directly in computer calculations. Instead they are approximated by manageable functions such as polynomials and piecewise polynomials. The general theory of the subject and its application to polynomial approximation are classical, but piecewise polynomials have become far more useful during the last twenty years. Thus many important theoretical properties have been found recently and many new techniques for the automatic calculation of approximations to prescribed accuracy have been developed. This book gives a thorough and coherent introduction to the theory that is the basis of current approximation methods. Professor Powell describes and analyses the main techniques of calculation supplying sufficient motivation throughout the book to make it accessible to scientists and engineers who require approximation methods for practical needs. Because the book is based on a course of lectures to third-year undergraduates in mathematics at Cambridge University, sufficient attention is given to theory to make it highly suitable as a mathematical textbook at undergraduate or postgraduate level.

Interpolation and Approximation

Author: Philip J. Davis

Publisher: Courier Corporation

ISBN: 0486624951

Category: Mathematics

Page: 393

View: 959

Intermediate-level survey covers remainder theory, convergence theorems, and uniform and best approximation. Other topics include least square approximation, Hilbert space, orthogonal polynomials, theory of closure and completeness, and more. 1963 edition.

Spectral Methods in MATLAB

Author: Lloyd N. Trefethen

Publisher: SIAM

ISBN: 0898714656

Category: Mathematics

Page: 165

View: 9472

Mathematics of Computing -- Numerical Analysis.

Spectra and Pseudospectra

The Behavior of Nonnormal Matrices and Operators

Author: Lloyd Nicholas Trefethen,Mark Embree

Publisher: Princeton University Press

ISBN: 9780691119465

Category: Mathematics

Page: 606

View: 9818

Pure and applied mathematicians, physicists, scientists, and engineers use matrices and operators and their eigenvalues in quantum mechanics, fluid mechanics, structural analysis, acoustics, ecology, numerical analysis, and many other areas. However, in some applications the usual analysis based on eigenvalues fails. For example, eigenvalues are often ineffective for analyzing dynamical systems such as fluid flow, Markov chains, ecological models, and matrix iterations. That's where this book comes in. This is the authoritative work on nonnormal matrices and operators, written by the authorities who made them famous. Each of the sixty sections is written as a self-contained essay. Each document is a lavishly illustrated introductory survey of its topic, complete with beautiful numerical experiments and all the right references. The breadth of included topics and the numerous applications that provide links between fields will make this an essential reference in mathematics and related sciences.

Introduction to Approximation Theory

Author: Elliott Ward Cheney

Publisher: Courier Corporation

ISBN: 9780821813744

Category: Mathematics

Page: 259

View: 1298

This volume contains historical background and discussion of results for each chapter, References, and an Index.

Design and Analysis of Approximation Algorithms

Author: Ding-Zhu Du,Ker-I Ko,Xiaodong Hu

Publisher: Springer Science & Business Media

ISBN: 1461417015

Category: Mathematics

Page: 440

View: 7293

This book is intended to be used as a textbook for graduate students studying theoretical computer science. It can also be used as a reference book for researchers in the area of design and analysis of approximation algorithms. Design and Analysis of Approximation Algorithms is a graduate course in theoretical computer science taught widely in the universities, both in the United States and abroad. There are, however, very few textbooks available for this course. Among those available in the market, most books follow a problem-oriented format; that is, they collected many important combinatorial optimization problems and their approximation algorithms, and organized them based on the types, or applications, of problems, such as geometric-type problems, algebraic-type problems, etc. Such arrangement of materials is perhaps convenient for a researcher to look for the problems and algorithms related to his/her work, but is difficult for a student to capture the ideas underlying the various algorithms. In the new book proposed here, we follow a more structured, technique-oriented presentation. We organize approximation algorithms into different chapters, based on the design techniques for the algorithms, so that the reader can study approximation algorithms of the same nature together. It helps the reader to better understand the design and analysis techniques for approximation algorithms, and also helps the teacher to present the ideas and techniques of approximation algorithms in a more unified way.

Chebyshev and Fourier Spectral Methods

Second Revised Edition

Author: John P. Boyd

Publisher: Courier Corporation

ISBN: 0486141926

Category: Mathematics

Page: 688

View: 6259

Completely revised text applies spectral methods to boundary value, eigenvalue, and time-dependent problems, but also covers cardinal functions, matrix-solving methods, coordinate transformations, much more. Includes 7 appendices and over 160 text figures.

Theory and Practice of Finite Elements

Author: Alexandre Ern,Jean-Luc Guermond

Publisher: Springer Science & Business Media

ISBN: 1475743556

Category: Mathematics

Page: 526

View: 6069

This text presenting the mathematical theory of finite elements is organized into three main sections. The first part develops the theoretical basis for the finite element methods, emphasizing inf-sup conditions over the more conventional Lax-Milgrim paradigm. The second and third parts address various applications and practical implementations of the method, respectively. It contains numerous examples and exercises.

Mathematics of Approximation

Author: Johan de De Villiers

Publisher: Springer Science & Business Media

ISBN: 9491216503

Category: Mathematics

Page: 406

View: 4927

The approximation of a continuous function by either an algebraic polynomial, a trigonometric polynomial, or a spline, is an important issue in application areas like computer-aided geometric design and signal analysis. This book is an introduction to the mathematical analysis of such approximation, and, with the prerequisites of only calculus and linear algebra, the material is targeted at senior undergraduate level, with a treatment that is both rigorous and self-contained. The topics include polynomial interpolation; Bernstein polynomials and the Weierstrass theorem; best approximations in the general setting of normed linear spaces and inner product spaces; best uniform polynomial approximation; orthogonal polynomials; Newton-Cotes , Gauss and Clenshaw-Curtis quadrature; the Euler-Maclaurin formula ; approximation of periodic functions; the uniform convergence of Fourier series; spline approximation,with an extensive treatment of local spline interpolation,and its application in quadrature. Exercises are provided at the end of each chapter

Approximation and Modeling with B-Splines

Author: Klaus HoÓllig,JÓorg HÓorner

Publisher: SIAM

ISBN: 1611972949

Category: Mathematics

Page: 214

View: 4074

B-splines are fundamental to approximation and data fitting, geometric modeling, automated manufacturing, computer graphics, and numerical simulation. With an emphasis on key results and methods that are most widely used in practice, this textbook provides a unified introduction to the basic components of B-spline theory: approximation methods (mathematics), modeling techniques (engineering), and geometric algorithms (computer science). A supplemental Web site will provide a collection of problems, some with solutions, slides for use in lectures, and programs with demos.

Model Reduction and Approximation

Theory and Algorithms

Author: Peter Benner,Albert Cohen,Mario Ohlberger,Karen Willcox

Publisher: SIAM

ISBN: 1611974828

Category: Science

Page: 412

View: 9208

Many physical, chemical, biomedical, and technical processes can be described by partial differential equations or dynamical systems. In spite of increasing computational capacities, many problems are of such high complexity that they are solvable only with severe simplifications, and the design of efficient numerical schemes remains a central research challenge. This book presents a tutorial introduction to recent developments in mathematical methods for model reduction and approximation of complex systems. Model Reduction and Approximation: Theory and Algorithms contains three parts that cover (I) sampling-based methods, such as the reduced basis method and proper orthogonal decomposition, (II) approximation of high-dimensional problems by low-rank tensor techniques, and (III) system-theoretic methods, such as balanced truncation, interpolatory methods, and the Loewner framework. It is tutorial in nature, giving an accessible introduction to state-of-the-art model reduction and approximation methods. It also covers a wide range of methods drawn from typically distinct communities (sampling based, tensor based, system-theoretic).?? This book is intended for researchers interested in model reduction and approximation, particularly graduate students and young researchers.

Approximation Algorithms

Author: Vijay V. Vazirani

Publisher: Springer Science & Business Media

ISBN: 3662045656

Category: Computers

Page: 380

View: 1010

Covering the basic techniques used in the latest research work, the author consolidates progress made so far, including some very recent and promising results, and conveys the beauty and excitement of work in the field. He gives clear, lucid explanations of key results and ideas, with intuitive proofs, and provides critical examples and numerous illustrations to help elucidate the algorithms. Many of the results presented have been simplified and new insights provided. Of interest to theoretical computer scientists, operations researchers, and discrete mathematicians.

Classical and Modern Numerical Analysis

Theory, Methods and Practice

Author: Azmy S. Ackleh,Edward James Allen,R. Baker Kearfott,Padmanabhan Seshaiyer

Publisher: CRC Press

ISBN: 9781420091588

Category: Mathematics

Page: 628

View: 804

Classical and Modern Numerical Analysis: Theory, Methods and Practice provides a sound foundation in numerical analysis for more specialized topics, such as finite element theory, advanced numerical linear algebra, and optimization. It prepares graduate students for taking doctoral examinations in numerical analysis. The text covers the main areas of introductory numerical analysis, including the solution of nonlinear equations, numerical linear algebra, ordinary differential equations, approximation theory, numerical integration, and boundary value problems. Focusing on interval computing in numerical analysis, it explains interval arithmetic, interval computation, and interval algorithms. The authors illustrate the concepts with many examples as well as analytical and computational exercises at the end of each chapter. This advanced, graduate-level introduction to the theory and methods of numerical analysis supplies the necessary background in numerical methods so that students can apply the techniques and understand the mathematical literature in this area. Although the book is independent of a specific computer program, MATLAB® code is available on the authors' website to illustrate various concepts.

Ordinary Differential Equations in Theory and Practice

Author: Robert Mattheij,Jaap Molenaar

Publisher: SIAM

ISBN: 0898715318

Category: Mathematics

Page: 405

View: 2068

In order to emphasize the relationships and cohesion between analytical and numerical techniques, Ordinary Differential Equations in Theory and Practice presents a comprehensive and integrated treatment of both aspects in combination with the modeling of relevant problem classes. This text is uniquely geared to provide enough insight into qualitative aspects of ordinary differential equations (ODEs) to offer a thorough account of quantitative methods for approximating solutions numerically, and to acquaint the reader with mathematical modeling, where such ODEs often play a significant role. Although originally published in 1995, the text remains timely and useful to a wide audience. It provides a thorough introduction to ODEs, since it treats not only standard aspects such as existence, uniqueness, stability, one-step methods, multistep methods, and singular perturbations, but also chaotic systems, differential-algebraic systems, and boundary value problems.

Orthogonal Polynomials in MATLAB

Exercises and Solutions

Author: Walter Gautschi

Publisher: SIAM

ISBN: 1611974305

Category: Science

Page: 335

View: 5392

Techniques for generating orthogonal polynomials numerically have appeared only recently, within the last 30 or so years.÷Orthogonal Polynomials in MATLAB: Exercises and Solutions÷describes these techniques and related applications, all supported by MATLAB programs, and presents them in a unique format of exercises and solutions designed by the author to stimulate participation. Important computational problems in the physical sciences are included as models for readers to solve their own problems.÷

Practical Applied Mathematics

Modelling, Analysis, Approximation

Author: Sam Howison

Publisher: Cambridge University Press

ISBN: 9780521842747

Category: Mathematics

Page: 326

View: 8577

Drawing from a wide variety of mathematical subjects, this book aims to show how mathematics is realised in practice in the everyday world. Dozens of applications are used to show that applied mathematics is much more than a series of academic calculations. Mathematical topics covered include distributions, ordinary and partial differential equations, and asymptotic methods as well as basics of modelling. The range of applications is similarly varied, from the modelling of hair to piano tuning, egg incubation and traffic flow. The style is informal but not superficial. In addition, the text is supplemented by a large number of exercises and sideline discussions, assisting the reader's grasp of the material. Used either in the classroom by upper-undergraduate students, or as extra reading for any applied mathematician, this book illustrates how the reader's knowledge can be used to describe the world around them.

Similitude and Approximation Theory

Author: S.J. Kline

Publisher: Springer Science & Business Media

ISBN: 3642616380

Category: Mathematics

Page: 229

View: 628

There are a number of reasons for producing this edition of Simili tude and Approximation Theory. The methodologies developed remain important in many areas of technical work. No other equivalent work has appeared in the two decades since the publication of the first edition. The materials still provide an important increase in understanding for first-year graduate students in engineering and for workers in research and development at an equivalent level. In addition, consulting experiences in a number of industries indi cate that many technical workers in research and development lack knowledge of the methodologies given in this work. This lack makes the work of planning and controlling computations and experiments less efficient in many cases. It also implies that the coordinated grasp of the phenomena (which is so critical to effective research and develop ment work) will be less than it might be. The materials covered in this work focus on the relationship between mathematical models and the physical reality such models are intended v vi Preface to the Springer Edition to portray. Understanding these relationships remains a key factor in simplifying and generalizing correlations, predictions, test programs, and computations. Moreover, as many teachers of engineering know, this kind of understanding is typically harder for students to develop than an understanding of either the mathematics or the physics alone.

The Princeton Companion to Applied Mathematics

Author: Nicholas J. Higham

Publisher: Princeton University Press

ISBN: 1400874475

Category: Mathematics

Page: 1016

View: 9905

This is the most authoritative and accessible single-volume reference book on applied mathematics. Featuring numerous entries by leading experts and organized thematically, it introduces readers to applied mathematics and its uses; explains key concepts; describes important equations, laws, and functions; looks at exciting areas of research; covers modeling and simulation; explores areas of application; and more. Modeled on the popular Princeton Companion to Mathematics, this volume is an indispensable resource for undergraduate and graduate students, researchers, and practitioners in other disciplines seeking a user-friendly reference book on applied mathematics. Features nearly 200 entries organized thematically and written by an international team of distinguished contributors Presents the major ideas and branches of applied mathematics in a clear and accessible way Explains important mathematical concepts, methods, equations, and applications Introduces the language of applied mathematics and the goals of applied mathematical research Gives a wide range of examples of mathematical modeling Covers continuum mechanics, dynamical systems, numerical analysis, discrete and combinatorial mathematics, mathematical physics, and much more Explores the connections between applied mathematics and other disciplines Includes suggestions for further reading, cross-references, and a comprehensive index