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Spline Functions on Triangulations

Spline Functions on Triangulations

Part of Encyclopedia of Mathematics and its Applications

  • Date Published: April 2007
  • availability: Available
  • format: Hardback
  • isbn: 9780521875929

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  • Spline functions are universally recognized as highly effective tools in approximation theory, computer-aided geometric design, image analysis, and numerical analysis. The theory of univariate splines is well known but this text is the first comprehensive treatment of the analogous bivariate theory. A detailed mathematical treatment of polynomial splines on triangulations is outlined, providing a basis for developing practical methods for using splines in numerous application areas. The detailed treatment of the Bernstein-Bézier representation of polynomials will provide a valuable source for researchers and students in CAGD. Chapters on smooth macro-element spaces will allow engineers and scientists using the FEM method to solve partial differential equations numerically with new tools. Workers in the geosciences will find new tools for approximation and data fitting on the sphere. Ideal as a graduate text in approximation theory, and as a source book for courses in computer-aided geometric design or in finite-element methods.

    • First book to offer a detailed treatment of bivariate splines
    • Provides a basis for developing practical methods for using splines in numerous application areas
    • Up-to-date and comprehensive account, suitable for mathematicians, statisticians, engineers, geoscientists, biologists and computer scientists working in academia or industry
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    Reviews & endorsements

    'If you need to know anything about multivariate splines this book will be yur first and surest source of information for years to come.' Mathematical Reviews

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    Product details

    • Date Published: April 2007
    • format: Hardback
    • isbn: 9780521875929
    • length: 608 pages
    • dimensions: 240 x 165 x 42 mm
    • weight: 0.99kg
    • contains: 115 b/w illus. 12 tables
    • availability: Available
  • Table of Contents

    Preface
    1. Bivariate polynomials
    2. Bernstein-Bézier methods for bivariate polynomials
    3. B-patches
    4. Triangulations and quadrangulations
    5. Bernstein-Bézier methods for spline spaces
    6. C1 Macro-element spaces
    7. C2 Macro-element spaces
    8. Cr Macro-element spaces
    9. Dimension of spline splines
    10. Approximation power of spline spaces
    11. Stable local minimal determining sets
    12. Bivariate box splines
    13. Spherical splines
    14. Approximation power of spherical splines
    15. Trivariate polynomials
    16. Tetrahedral partitions
    17. Trivariate splines
    18. Trivariate macro-element spaces
    Bibliography
    Index.

  • Authors

    Ming-Jun Lai, University of Georgia
    Ming-Jun Lai is a Professor of Mathematics at the University of Georgia.

    Larry L. Schumaker, Vanderbilt University, Tennessee
    Larry Schumaker is the Stevenson Professor of Mathematics at Vanderbilt University.

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