Scattered Data Approximation

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

• 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.

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