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Scattered Data Approximation

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ISBN-10: 0521843359

ISBN-13: 9780521843355

Edition: 2004

Authors: Holger Wendland, P. G. Ciarlet, A. Iserles, R. V. Kohn, M. H. Wright

List price: $155.00
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Description:

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.
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Book details

List price: $155.00
Copyright year: 2004
Publisher: Cambridge University Press
Publication date: 12/13/2004
Binding: Hardcover
Pages: 348
Size: 6.25" wide x 9.00" long x 0.75" tall
Weight: 1.540
Language: English

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
Stability
Optimal recovery
Data structures
Numerical methods
Generalized interpolation
Interpolation on spheres and other manifolds