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Multivariate Approximation and Splines

  • Conference proceedings
  • © 1997

Overview

Editors:
  1. Günther Nürnberger

    1. Fakultät für Mathematik und Informatik, Universität Mannheim, Mannheim, Germany

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  2. Jochen W. Schmidt

    1. Institut für Numerische Mathematik, Technische Universität Dresden, Dresden, Germany

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  3. Guido Walz

    1. Fakultät für Mathematik und Informatik, Universität Mannheim, Mannheim, Germany

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Part of the book series: International Series of Numerical Mathematics (ISNM, volume 125)

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Table of contents (24 papers)

  1. Front Matter

    Pages i-x
    Download chapter PDF

  2. Multivariate Inequalities of Kolmogorov Type and Their Applications

    • V. F. Babenko, V. A. Kofanov, S. A. Pichugov
    Pages 1-12

  3. Monotone Iterative Technique for Impulsive Differential-Difference Equations with Variable Impulsive Perturbations

    • Drumi Bainov, Angel Dishliev, Snezhana Hristova
    Pages 13-27

  4. Multivariate Cosine Wavelets

    • Kai Bittner, Charles K. Chui, Jürgen Prestin
    Pages 29-43

  5. On Almost Interpolation by Multivariate Splines

    • Oleg Davydov, Manfred Sommer, Hans Strauss
    Pages 45-58

  6. Locally Linearly Independent Systems and Almost Interpolation

    • Oleg Davydov, Manfred Sommer, Hans Strausβ
    Pages 59-72

  7. Exponential-type Approximation in Multivariate Harmonic Hilbert Spaces

    • Franz-Jürgen Delvos
    Pages 73-82

  8. Interpolation by Continuous Function Spaces

    • Manfred von Golitschek
    Pages 83-88

  9. Discrete Characterization of Besov Spaces and Its Applications to Stochastics

    • Anna Kamont
    Pages 89-98

  10. One-Sided Approximation and Interpolation Operators Generating Hyperbolic Sigma-Pi Neural Networks

    • Burkhard Lenze
    Pages 99-112

  11. Unconstrained Minimization of Quadratic Splines and Applications

    • Wu Li
    Pages 113-128

  12. Interpolation by Translates of a Basis Function

    • Will Light
    Pages 129-140

  13. On the Sup-norm Condition Number of the Multivariate Triangular Bernstein Basis

    • Tom Lyche, Karl Scherer
    Pages 141-151

  14. Integration Methods of Clenshaw-Curtis Type, Based on Four Kinds of Chebyshev Polynomials

    • J. C. Mason, E. Venturino
    Pages 153-165

  15. Tensor Products of Convex Cones

    • Bernd Mulansky
    Pages 167-176

  16. The Curse of Dimension and a Universal Method For Numerical Integration

    • Erich Novak, Klaus Ritter
    Pages 177-187

  17. Interpolation by Bivariate Splines on Crosscut Partitions

    • Günther Nürnberger, Oleg V. Davydov, Guido Walz, Frank Zeilfelder
    Pages 189-203

  18. Necessary and Sufficient Conditions for Orthonormality of Scaling Vectors

    • Gerlind Plonka
    Pages 205-218

  19. Trigonometric Preconditioners for Block Toeplitz Systems

    • Daniel Potts, Gabriele Steidl, Manfred Tasche
    Pages 219-234

  20. The Average Size of Certain Gram-Determinants and Interpolation on Non-Compact Sets

    • Manfred Reimer
    Pages 235-243
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Keywords

About this book

This book contains the refereed papers which were presented at the interna­ tional conference on "Multivariate Approximation and Splines" held in Mannheim, Germany, on September 7-10,1996. Fifty experts from Bulgaria, England, France, Israel, Netherlands, Norway, Poland, Switzerland, Ukraine, USA and Germany participated in the symposium. It was the aim of the conference to give an overview of recent developments in multivariate approximation with special emphasis on spline methods. The field is characterized by rapidly developing branches such as approximation, data fit­ ting, interpolation, splines, radial basis functions, neural networks, computer aided design methods, subdivision algorithms and wavelets. The research has applications in areas like industrial production, visualization, pattern recognition, image and signal processing, cognitive systems and modeling in geology, physics, biology and medicine. In the following, we briefly describe the contents of the papers. Exact inequalities of Kolmogorov type which estimate the derivatives of mul­ the paper of BABENKO, KOFANovand tivariate periodic functions are derived in PICHUGOV. These inequalities are applied to the approximation of classes of mul­ tivariate periodic functions and to the approximation by quasi-polynomials. BAINOV, DISHLIEV and HRISTOVA investigate initial value problems for non­ linear impulse differential-difference equations which have many applications in simulating real processes. By applying iterative techniques, sequences of lower and upper solutions are constructed which converge to a solution of the initial value problem.

Editors and Affiliations

  • Fakultät für Mathematik und Informatik, Universität Mannheim, Mannheim, Germany

    Günther Nürnberger, Guido Walz

  • Institut für Numerische Mathematik, Technische Universität Dresden, Dresden, Germany

    Jochen W. Schmidt

Bibliographic Information

  • Book Title: Multivariate Approximation and Splines

  • Editors: Günther Nürnberger, Jochen W. Schmidt, Guido Walz

  • Series Title: International Series of Numerical Mathematics

  • DOI: https://doi.org/10.1007/978-3-0348-8871-4

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Basel AG 1997

  • Hardcover ISBN: 978-3-7643-5654-5Published: 23 September 1997

  • Softcover ISBN: 978-3-0348-9808-9Published: 22 November 2012

  • eBook ISBN: 978-3-0348-8871-4Published: 06 December 2012

  • Series ISSN: 0373-3149

  • Series E-ISSN: 2296-6072

  • Edition Number: 1

  • Number of Pages: X, 326

  • Topics: Analysis

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