Scattered Data Approximation


Scattered Data Approximation

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.


 Reviews:

"Scattered Data Approximation provides the most complete up-to-date reference on multivariate scattered data approximation from an RBF/mesh-free point of view...I would like to close with a high recommendation of this book. It should be part of anyone's library on modern multivariate approximation techniques."
SIAM Review

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

No references available.