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Spline Functions and Multivariate Interpolations

  • B. D. Bojanov
  • H. A. Hakopian
  • A. A. Sahakian

Part of the Mathematics and Its Applications book series (MAIA, volume 248)

Table of contents

  1. Front Matter
    Pages i-ix
  2. B. D. Bojanov, H. A. Hakopian, A. A. Sahakian
    Pages 1-18
  3. B. D. Bojanov, H. A. Hakopian, A. A. Sahakian
    Pages 19-27
  4. B. D. Bojanov, H. A. Hakopian, A. A. Sahakian
    Pages 28-44
  5. B. D. Bojanov, H. A. Hakopian, A. A. Sahakian
    Pages 45-66
  6. B. D. Bojanov, H. A. Hakopian, A. A. Sahakian
    Pages 67-81
  7. B. D. Bojanov, H. A. Hakopian, A. A. Sahakian
    Pages 82-108
  8. B. D. Bojanov, H. A. Hakopian, A. A. Sahakian
    Pages 109-116
  9. B. D. Bojanov, H. A. Hakopian, A. A. Sahakian
    Pages 117-131
  10. B. D. Bojanov, H. A. Hakopian, A. A. Sahakian
    Pages 132-148
  11. B. D. Bojanov, H. A. Hakopian, A. A. Sahakian
    Pages 149-162
  12. B. D. Bojanov, H. A. Hakopian, A. A. Sahakian
    Pages 163-197
  13. B. D. Bojanov, H. A. Hakopian, A. A. Sahakian
    Pages 198-205
  14. B. D. Bojanov, H. A. Hakopian, A. A. Sahakian
    Pages 206-230
  15. B. D. Bojanov, H. A. Hakopian, A. A. Sahakian
    Pages 231-264
  16. Back Matter
    Pages 265-278

About this book

Introduction

Spline functions entered Approximation Theory as solutions of natural extremal problems. A typical example is the problem of drawing a function curve through given n + k points that has a minimal norm of its k-th derivative. Isolated facts about the functions, now called splines, can be found in the papers of L. Euler, A. Lebesgue, G. Birkhoff, J. Favard, L. Tschakaloff. However, the Theory of Spline Functions has developed in the last 30 years by the effort of dozens of mathematicians. Recent fundamental results on multivariate polynomial interpolation and multivari­ ate splines have initiated a new wave of theoretical investigations and variety of applications. The purpose of this book is to introduce the reader to the theory of spline functions. The emphasis is given to some new developments, such as the general Birkoff's type interpolation, the extremal properties of the splines and their prominant role in the optimal recovery of functions, multivariate interpolation by polynomials and splines. The material presented is based on the lectures of the authors, given to the students at the University of Sofia and Yerevan University during the last 10 years. Some more elementary results are left as excercises and detailed hints are given.

Keywords

Approximation Interpolation algebra approximation theory function

Authors and affiliations

  • B. D. Bojanov
    • 1
  • H. A. Hakopian
    • 2
  • A. A. Sahakian
    • 2
  1. 1.Department of MathematicsUniversity of SofiaSofiaBulgaria
  2. 2.Department of MathematicsYerevan UniversityYerevanArmenia

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-015-8169-1
  • Copyright Information Springer Science+Business Media B.V. 1993
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-4259-0
  • Online ISBN 978-94-015-8169-1
  • Buy this book on publisher's site
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