Scattered Data Approximation (Cambridge Monographs on Applied and Computational Mathematics)

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If for any reason your order is not available to ship, you will not be charged. Your order is also backed by our In-Stock Guarantee! What makes Biblio different? Sign In Register Help Cart 0. Search Results Results 1 -6 of 6. This book introduces the mathematical concept of PDEs for virtual image restoration. It gives the full picture, from the first modelling steps originating in Gestalt theory and arts restoration to the analysis of resulting PDE models, numerical realisation and real-world application.

This broad approach also gives insight into functional analysis, variational calculus, optimisation and numerical analysis and will appeal to researchers and graduate students in mathematics with an interest in image processing and mathematical analysis. Micchelli , Yuesheng Xu https: The recent appearance of wavelets as a new computational tool in applied mathematics has given a new impetus to the field of numerical analysis of Fredholm integral equations. This book gives an account of the state of the art in the study of fast multiscale methods for solving these equations based on wavelets.

The authors begin by introducing essential concepts and describing conventional numerical methods. They then develop fast algorithms and apply these to solving linear, nonlinear Fredholm integral equations of the second kind, ill-posed integral equations of the first kind and eigen-problems of compact integral operators.

Theorems of functional analysis used throughout the book are summarised in the appendix. The book is an essential reference for practitioners wishing to use the new techniques.

It may also be used as a text, with the first five chapters forming the basis of a one-semester course for advanced undergraduates or beginning graduates. Most well-known solution techniques for differential equations exploit symmetry in some form. Systematic methods have been developed for finding and using symmetries, first integrals and conservation laws of a given differential equation.

Here the author explains how to extend these powerful methods to difference equations, greatly increasing the range of solvable problems.


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Beginning with an introduction to elementary solution methods, the book gives readers a clear explanation of exact techniques for ordinary and partial difference equations. The informal presentation is suitable for anyone who is familiar with standard differential equation methods. No prior knowledge of difference equations or symmetry is assumed. The author uses worked examples to help readers grasp new concepts easily.

There are exercises of varying difficulty and suggestions for further reading.

Scattered data approximation

The book goes to the cutting edge of research; its many new ideas and methods make it a valuable reference for researchers in the field. Greedy Approximation Vladimir Temlyakov https: This first book on greedy approximation gives a systematic presentation of the fundamental results. It also contains an introduction to two hot topics in numerical mathematics: Nonlinear approximation is becoming increasingly important, especially since two types are frequently employed in applications: The fundamental question of nonlinear approximation is how to devise good constructive methods algorithms and recent results have established that greedy type algorithms may be the solution.

The author has drawn on his own teaching experience to write a book ideally suited to graduate courses.

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The reader does not require a broad background to understand the material. Important open problems are included to give students and professionals alike ideas for further research. Modern Computer Arithmetic Richard P. Brent , Paul Zimmermann https: Modern Computer Arithmetic focuses on arbitrary-precision algorithms for efficiently performing arithmetic operations such as addition, multiplication and division, and their connections to topics such as modular arithmetic, greatest common divisors, the Fast Fourier Transform FFT , and the computation of elementary and special functions.

Brent and Zimmermann present algorithms that are ready to implement in your favourite language, while keeping a high-level description and avoiding too low-level or machine-dependent details. The book is intended for anyone interested in the design and implementation of efficient high-precision algorithms for computer arithmetic, and more generally efficient multiple-precision numerical algorithms. It may also be used in a graduate course in mathematics or computer science, for which exercises are included.

These vary considerably in difficulty, from easy to small research projects, and expand on topics discussed in the text. Solutions to selected exercises are available from the authors. This book explains recent results in the theory of moving frames that concern the symbolic manipulation of invariants of Lie group actions. In particular, theorems concerning the calculation of generators of algebras of differential invariants, and the relations they satisfy, are discussed in detail.

The author demonstrates how new ideas lead to significant progress in two main applications: The expository language used here is primarily that of undergraduate calculus rather than differential geometry, making the topic more accessible to a student audience. More sophisticated ideas from differential topology and Lie theory are explained from scratch using illustrative examples and exercises. This book is ideal for graduate students and researchers working in differential equations, symbolic computation, applications of Lie groups and, to a lesser extent, differential geometry.

Sure to be influential, this book lays the foundations for the use of algebraic geometry in statistical learning theory.

Many widely used statistical models and learning machines applied to information science have a parameter space that is singular: Algebraic geometry and singularity theory provide the necessary tools for studying such non-smooth models. Four main formulas are established: The goal of learning theory is to approximate a function from sample values.

To attain this goal learning theory draws on a variety of diverse subjects, specifically statistics, approximation theory, and algorithmics. Ideas from all these areas blended to form a subject whose many successful applications have triggered a rapid growth during the last two decades. This is the first book to give a general overview of the theoretical foundations of the subject emphasizing the approximation theory, while still giving a balanced overview.

Unlocking potential with the best learning and research solutions

It is based on courses taught by the authors, and is reasonably self-contained so will appeal to a broad spectrum of researchers in learning theory and adjacent fields. It will also serve as an introduction for graduate students and others entering the field, who wish to see how the problems raised in learning theory relate to other disciplines. Hesthaven , Sigal Gottlieb , David Gottlieb https: Spectral methods are well-suited to solve problems modeled by time-dependent partial differential equations: This class-tested introduction, the first on the subject, is ideal for graduate courses, or self-study.

This book gives a self-contained, complete introduction into this subject. Each chapter ends with a section giving information on the historical background and hints for further reading. It concentrates on truly meshless methods such as radial basis functions, moving least squares, and partitions of unity.

Download The Theory of Composites Cambridge Monographs on Applied and Computational Mathematics Book

The book starts with an overview on typical applications of scattered data approximation, coming from surface reconstruction, fluid-structure interaction, and the numerical solution of partial differential equations. It then leads the reader from basic properties to the current state of research, addressing all important issues, such as existence, uniqueness, approximation properties, numerical stability, and efficient implementation.

Complete proofs are included, making this perfectly suited for graduate courses on multivariate approximation and it can be used to support courses in computer-aided geometric design, and meshless methods for partial differential equations.

Scattered data approximation : Sussex Research Online

This complete self-contained introduction to the theory of scattered data approximation brings together much of the necessary background material in one source. It also provides students with complete proofs to the theory developed within.


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  • Scattered data approximation | Numerical analysis | Cambridge University Press.
  • Additional Details Series Volume Number. Table Of Content 1.