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  1. Home
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  3. Scattered Data Approximation
  • Cited by 486
Publisher:
Cambridge University Press
Online publication date:
February 2010
Print publication year:
2004
Online ISBN:
9780511617539
DOI:
https://doi.org/10.1017/CBO9780511617539
Subjects:
Mathematics, Computational Science, Numerical Analysis and Computational Science
Series:
Cambridge Monographs on Applied and Computational Mathematics (17)
Information

Book description

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

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.'

Source: 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.'

Source: Numerical Algorithms

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