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Scattered Data Approximation : Cambridge Monographs on Applied and Computational Mathematics - Holger Wendland

Scattered Data Approximation

Cambridge Monographs on Applied and Computational Mathematics


Published: 1st December 2004
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Many practical applications require the reconstruction of a multivariate function from discrete, unstructured data. This book gives a self-contained, complete introduction into this subject. It concentrates on truly meshless methods such as radial basis functions, moving least squares, and partitions of unity. 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. Each chapter ends with a section giving information on the historical background and hints for further reading. 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.

' ... designed as a comprehensive and self-contained introduction to the field of multivariate scattered data approximation ... The book offers an interesting reading for both the beginner and the specialist ... throughout its variety of topics and its careful exposition, this book will appeal to everyone interested in the theory and numerical applications of meshless methods for scattered data approximation.' Zentralblatt MATH 'I highly recommend it for a graduate course on multivariate approximation theory, computer-aided geometric design, and meshless methods for partial differential equations.' Numerical Algorithms

Applications and motivations
Hear spaces and multivariate polynomials
Local polynomial reproduction
Moving least squares
Auxiliary tools from analysis and measure theory
Positive definite functions
Completely monotine functions
Conditionally positive definite functions
Compactly supported functions
Native spaces
Error estimates for radial basis function interpolation
Optimal recovery
Data structures
Numerical methods
Generalized interpolation
Interpolation on spheres and other manifolds
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521843355
ISBN-10: 0521843359
Series: Cambridge Monographs on Applied and Computational Mathematics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 348
Published: 1st December 2004
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 22.8 x 15.2  x 2.4
Weight (kg): 0.69