Spline Functions and Multivariate Interpolations

Spline Functions and Multivariate Interpolations

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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.
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Product details

  • Hardback | 278 pages
  • 162.6 x 238.8 x 22.9mm | 476.28g
  • Dordrecht, Netherlands
  • English
  • 1993 ed.
  • X, 278 p.
  • 0792322290
  • 9780792322290

Table of contents

Series Editor's Preface. Preface. 1. Interpolation by Algebraic Polynomials. 2. The Space of Splines. 3. B-Splines. 4. Interpolation by Spline Functions. 5. Natural Spline Functions. 6. Perfect Splines. 7. Monosplines. 8. Periodic Splines. 9. Multivariate B-Splines and Truncated Powers. 10. Multivariate Spline Functions and Divided Differences. 11. Box Splines. 12. Multivariate Mean Value Interpolation. 13. Multivariate Polynomial Interpolations arising by Hyperplanes. 14. Multivariate Pointwise Interpolation. References. Index. Notation.
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