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Modern Developments in Multivariate Approximation

5th International Conference, Witten-Bommerholz (Germany), September 2002

  • Conference proceedings
  • © 2003

Overview

Editors:
  1. Werner Haussmann

    1. Mathematisches Institut, Gerhard-Mercator-Universität Duisburg, Duisburg, Germany

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  2. Kurt Jetter

    1. Institut für Angewandte Mathematik und Statistik, Universität Hohenheim, Stuttgart, Germany

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  3. Manfred Reimer

    1. Fachbereich Mathematik, Universität Dortmund, Dortmund, Germany

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  4. Joachim Stöckler

    1. Fachbereich Mathematik, Universität Dortmund, Dortmund, Germany

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  • Provides an overview of state-of-the-art developments in a highly relevant field of applied mathematics with many links to computer science and geophysics

Part of the book series: International Series of Numerical Mathematics (ISNM, volume 145)

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Table of contents (18 papers)

  1. Front Matter

    Pages 1-20
    Download chapter PDF

  2. Multivariate Approximation Methods for the Pricing of Catastrophe—Linked Bonds

    • Hansjörg Albrecher, Jürgen Hartinger, Robert F. Tichy
    Pages 21-39

  3. Note on a Generalized Invariance Principle and its Relevance for Cap Discrepancy and Energy

    • Johann S. Brauchart
    Pages 41-55

  4. On Properties of Nonstationary Divided Difference Vector Subdivision Schemes

    • Maria Charina, Costanza Conti
    Pages 57-69

  5. Multivariate Balanced Vector-Valued Refinable Functions

    • Charles K. Chui, Qingtang Jiang
    Pages 71-102

  6. Transfinite Interpolation by Blending Functions, Best One-Sided L1-Approximation, and Cubature Formulae

    • Dimiter P. Dryanov
    Pages 103-123

  7. Refining Oscillatory Signals by Non—Stationary Subdivision Schemes

    • Nira Dyn, David LevinAriel Luzzatto
    Pages 125-142

  8. Asymptotic Error Expansions for Schoenberg Type Operators

    • Karol Dziedziul, Kurt Jetter
    Pages 143-152

  9. On the Approximation Order and Numerical Stability of Local Lagrange Interpolation by Polyharmonic Splines

    • Armin Iske
    Pages 153-165

  10. Isolated Singularities of Harmonic Functions

    • Lavi Karp, Harold S. Shapiro
    Pages 167-174

  11. Two Applications of Adaptive Wavelet Methods

    • Angela Kunoth
    Pages 175-201

  12. Almost Interpolation and Radial Basis Functions

    • Alain Le Méhauté
    Pages 203-214

  13. Fundamental Splines on Triangulations

    • GÜnther NÜrnberger, Frank Zeilfelder
    Pages 215-233

  14. Integer DCT—II by Lifting Steps

    • Gerlind Plonka, Manfred Tasche
    Pages 235-252

  15. Approximation of Density Functions and Reconstruction of the Approximant

    • Manfred Reimer
    Pages 253-261

  16. On Some Multivariate Quadratic Spline Quasi—Interpolants on Bounded Domains

    • Paul Sablonnière
    Pages 263-278

  17. How to Generate Smoother Refinable Functions from Given Ones

    • Tomas Sauer
    Pages 279-293

  18. Reconstructing Multivariate Functions from Large Data Sets

    • Holger Wendland
    Pages 295-308

  19. Three Scale Versus Matrix Refinement Equations

    • Georg Zimmermann
    Pages 309-319
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Keywords

About this book

This volume contains a selection of eighteen peer-reviewed articles that were presented at the 5th International Conference on Multivariate Approximation, held in Witten-Bommerholz in September 2002. The contributions cover recent developments of constructive approximation on manifolds, approximation by splines and kernels, subdivision techniques and wavelet methods.
The main topics are:
- applications of multivariate approximation in finance
- approximation and stable reconstruction of images, data reduction
- multivariate splines for Lagrange interpolation and quasi-interpolation
- radial basis functions
- spherical point sets
- refinable function vectors and non-stationary subdivision
- applications of adaptive wavelet methods
- blending functions and cubature formulae
- singularities of harmonic functions
The book provides an overview of state-of-the-art developments in a highly relevant field of applied mathematics, with many links to computerscience and geophysics.

Editors and Affiliations

  • Mathematisches Institut, Gerhard-Mercator-Universität Duisburg, Duisburg, Germany

    Werner Haussmann

  • Institut für Angewandte Mathematik und Statistik, Universität Hohenheim, Stuttgart, Germany

    Kurt Jetter

  • Fachbereich Mathematik, Universität Dortmund, Dortmund, Germany

    Manfred Reimer, Joachim Stöckler

Bibliographic Information

  • Book Title: Modern Developments in Multivariate Approximation

  • Book Subtitle: 5th International Conference, Witten-Bommerholz (Germany), September 2002

  • Editors: Werner Haussmann, Kurt Jetter, Manfred Reimer, Joachim Stöckler

  • Series Title: International Series of Numerical Mathematics

  • DOI: https://doi.org/10.1007/978-3-0348-8067-1

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Birkh�user Verlag P.O. Box 133, CH-4010 Basel, Switzerland 2003

  • Hardcover ISBN: 978-3-7643-2195-6Published: 24 October 2003

  • eBook ISBN: 978-3-0348-8067-1Published: 12 June 2019

  • Series ISSN: 0373-3149

  • Series E-ISSN: 2296-6072

  • Edition Number: 1

  • Number of Pages: XX, 299

  • Topics: Calculus of Variations and Optimal Control; Optimization

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