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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.
- Sales Rank: #2609773 in Books
- Published on: 2010-02-11
- Original language: English
- Number of items: 1
- Dimensions: 9.02" h x .79" w x 5.98" l, 1.12 pounds
- Binding: Paperback
- 348 pages
Review
"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
About the Author
Holger Wendland is Associate Professor at the Institute for Numerical and Applied Mathematics at Georg-August-University, Gottingen.
Most helpful customer reviews
6 of 6 people found the following review helpful.
Excellent introduction to radial basis functions
By Colin Fox
I don't know if math books are allowed to be described as "page turners" but that's how I found this book. I read it cover to cover and came away knowing most everything I wanted to about radial basis functions and how to use them. I found the coverage of material to be well-motivated, complete, accurate, and very well written. If I were picky I would say that the author gets a bit carried away with measure theory formalism, particularly in the characterization of positive functions, but that's a minor complaint about an excellent book. I'd say it is a must-have for the library of anyone interested in theory and application of RBFs.
0 of 0 people found the following review helpful.
Excellent Coverage of RBF Approximations
By Joel
This textbook covers everything one would want to know about approximations with radial basis functions. This thorough treatment discusses approximations, completely and conditionally positive definite functions, compactly supported radial basis functions, the Gaussian radial basis functions, native spaces and convergence rates. It also discusses numerical methods, and a few other topics.
What is nice about the textbook is that it does not skimp on proofs or details. The reading is straightforward and well motivated. After considering several texts and papers, I found that this book has everything I was looking for.
The closest book I use as a companion is Fasshauer's text "Meshfree Approximation Methods with Matlab." Fasshauer covers similar materials and frequently cites this author's papers. Both are good texts. Fasshauer covers a little bit more material, but overall does not prove theorems to the same detail as Wendland.
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