Scattered Data Approximation

Erscheinungsjahr 2009
ISBN: 978-0-521-13101-8
Verlag: Cambridge University Press

Buch, Englisch, Band 17, 348 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 565 g

Reihe: Cambridge Monographs on Applied and Computational Mathematics

• A complete survey on multivariate scattered data approximation
• Covers theory behind, and implementation of, techniques
• Contains complete proofs of all theorems and covers several illustrating examples
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.

Autoren/Hrsg.

Wendland, Holger

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Mathematik | Informatik EDV | Informatik Professionelle Anwendung Computer-Aided Design (CAD)
• Mathematik | Informatik Mathematik Mathematische Analysis Moderne Anwendungen der Analysis

Inhaltsverzeichnis

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.