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Multivariate Splines

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Multivariate Splines

Multivariate Splines

Charles K. Chui
July 1988
Paperback
9780898712261
$67.99
USD
Paperback
    Description

    The subject of multivariate splines has become a rapidly growing field of mathematical research. The author presents the subject from an elementary point of view that parallels the theory and development of univariate spline analysis. To compensate for the missing proofs and details, an extensive bibliography has been included. There is a presentation of open problems with an emphasis on the theory and applications to computer-aided design, data analysis, and surface fitting. Applied mathematicians and engineers working in the areas of curve fitting, finite element methods, computer-aided geometric design, signal processing, mathematical modelling, computer-aided design, computer-aided manufacturing, and circuits and systems will find this monograph essential to their research.

    Reviews & endorsements

    'This is a narration about the multivariate splines, mostly without proofs and details, with many examples treating important particular cases, with many formulas and recurrence relations, complete description of computational algorithms, and an extensive bibliography. The book would appeal to students, scientists and engineers.' B. Boyanov, Mathematical Reviews

    See more reviews

    Product details

    July 1988
    Paperback
    9780898712261
    195 pages
    252 × 173 × 14 mm
    0.344kg
    This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.

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    Contents

    Table of Contents

    • Univariate Splines: B-splines and truncated powers on uniform mesh
    • Univariate spline spaces
    • Some basic properties of B-splines
    • B-spline series
    • Computation of B-splines
    • Box Splines and Multivariate Truncated Powers: Box splines
    • Basic properties of box splines
    • Multivariate truncated powers
    • Box spline series
    • Bivariate Splines on Three and Four Directional Meshes: Dimension
    • Locally supported splines
    • Minimal and quasi-minimal supported bivariate splines
    • Bases and approximation order
    • Quasi-Interpolation Schemes: The commutator operator
    • Polynomial-generating formulas
    • Construction of quasi-interpolants
    • Neumann series approach
    • Multivariate Interpolation: Interpolation by polynomials
    • Lagrange interpolation by multivariate splines
    • Cardinal interpolation with nonsingular
    • Cardinal interpolation with singular
    • Scaled cardinal interpolation
    • Shape-Preserving Approximation and Other Applications: Shape-preserving approximation by box spline series
    • Shape-preserving quasi-interpolation and interpolation
    • Application of CAGD
    • Reconstruction of gradient fields
    • Applications to signal processing.
      • Show more
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    Additional Information
    About the authors
      Author
    • Charles K. Chui

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