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Scattered Data Approximation

$155.00 (P)

Part of Cambridge Monographs on Applied and Computational Mathematics

  • Date Published: December 2004
  • availability: Available
  • format: Hardback
  • isbn: 9780521843355

$ 155.00 (P)

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About the Authors
  • 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.

    • 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
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    Reviews & endorsements

    "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

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    Product details

    • Date Published: December 2004
    • format: Hardback
    • isbn: 9780521843355
    • length: 348 pages
    • dimensions: 229 x 152 x 24 mm
    • weight: 0.68kg
    • availability: Available
  • Table of Contents

    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.

  • Author

    Holger Wendland, Georg-August-Universität, Göttingen, Germany

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