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Scattered data approximation

Author: Holger Wendland
Publisher: Cambridge, UK ; New York : Cambridge University Press, 2005.
Series: Cambridge monographs on applied and computational mathematics, 17.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Wendland, Holger, 1968-
Scattered data approximation.
Cambridge, UK ; New York : Cambridge University Press, 2005
(DLC) 2004049270
(OCoLC)54913412
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Holger Wendland
ISBN: 9780511265792 0511265794 0511263511 9780511263514 0511265077 9780511265075
OCLC Number: 85269234
Description: 1 online resource (x, 336 pages) : illustrations.
Contents: Introduction --
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 and radial basis function interpolation --
Stability --
Optimal recovery --
Data structures --
Numerical methods --
Generalized interpolation --
Interpolation on spheres and other manifolds.
Series Title: Cambridge monographs on applied and computational mathematics, 17.
Responsibility: Holger Wendland.
More information:

Abstract:

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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