Scattered Data Approximation

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Dezember 2004



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.


1. Applications and motivations; 2. Hear spaces and multivariate polynomials; 3. Local polynomial reproduction; 4. Moving least squares; 5. Auxiliary tools from analysis and measure theory; 6. Positive definite functions; 7. Completely monotine functions; 8. Conditionally positive definite functions; 9. Compactly supported functions; 10. Native spaces; 11. Error estimates for radial basis function interpolation; 12. Stability; 13. Optimal recovery; 14. Data structures; 15. Numerical methods; 16. Generalised interpolation; 17. Interpolation on spheres and other manifolds.


Holger Wendland is Associate Professor at the Institute for Numerical and Applied Mathematics at Georg-August-University, Gottingen.


Review of the hardback: ' ... 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 Review of the hardback: '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
EAN: 9780521843355
ISBN: 0521843359
Untertitel: 'Cambridge Monographs on Applie'. Sprache: Englisch.
Erscheinungsdatum: Dezember 2004
Seitenanzahl: 336 Seiten
Format: gebunden
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