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Multivariate Approximation and Splines

  • Günther Nürnberger
  • Jochen W. Schmidt
  • Guido Walz

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

Table of contents

  1. Front Matter
    Pages i-x
  2. V. F. Babenko, V. A. Kofanov, S. A. Pichugov
    Pages 1-12
  3. Kai Bittner, Charles K. Chui, Jürgen Prestin
    Pages 29-43
  4. Oleg Davydov, Manfred Sommer, Hans Strauss
    Pages 45-58
  5. Oleg Davydov, Manfred Sommer, Hans Strausβ
    Pages 59-72
  6. Manfred von Golitschek
    Pages 83-88
  7. Bernd Mulansky
    Pages 167-176
  8. Günther Nürnberger, Oleg V. Davydov, Guido Walz, Frank Zeilfelder
    Pages 189-203
  9. Daniel Potts, Gabriele Steidl, Manfred Tasche
    Pages 219-234
  10. Robert Schaback
    Pages 245-258
  11. Gerhard Schmeisser, Jürgen J. Voss
    Pages 275-288
  12. Jochen W. Schmidt, Marion Walther
    Pages 289-305
  13. Joachim Stöckler
    Pages 307-320
  14. Back Matter
    Pages 321-326

About these proceedings

Introduction

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.

Keywords

Division approximation differential equation equation function integration interpolation optimization

Editors and affiliations

  • Günther Nürnberger
    • 1
  • Jochen W. Schmidt
    • 2
  • Guido Walz
    • 1
  1. 1.Fakultät für Mathematik und InformatikUniversität MannheimMannheimGermany
  2. 2.Institut für Numerische MathematikTechnische Universität DresdenDresdenGermany

Bibliographic information

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