Bibliographic Information

Birkhoff interpolation

G.G. Lorentz, K. Jetter, S.D. Riemenschneider

(Encyclopedia of mathematics and its applications / edited by G.-C. Rota, v. 19 . Section, Interpolation and approximation)

Cambridge University Press, 2009

  • : pbk

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Note

First published by Cambridge University Press 1984, This digitally printed vrsion 2009

Bibliography: p. 220-231

Includes indexes

Description and Table of Contents

Description

This reference book provides the main definitions, theorems and techniques in the theory of Birkhoff interpolation by polynomials. The book begins with an article by G. G. Lorentz that discusses some of the important developments in approximation and interpolation in the last twenty years. It presents all the basic material known at the present time in a unified manner. Topics discussed include; applications of Birkhoff interpolation to approximation theory, quadrature formulas and Chebyshev systems; lacunary interpolation at special knots and an introduction to the theory of Birkhoff interpolation by splines.

Table of Contents

  • 1. Basic definitions and properties
  • 2. Further elementary theorems
  • 3. Coalescence of rows
  • 4. Applications of coalescence
  • 5. Rolle extensions and independent sets of knots
  • 6. Singular matrices
  • 7. Zeros of Birkhoff splines
  • 8. Almost-Hermitian matrices
  • special three-row matrices
  • 9. Applications
  • 10. Birkhoff quadrature formulas
  • 11. Interpolation at the roots of unity
  • 12. Turan's problem of interpolation
  • 13. Birkhoff interpolation by splines
  • 14. Regularity theorems and self-dual problems
  • Bibliography and references
  • Indexes.

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Details

  • NCID
    BB04489300
  • ISBN
    • 9780521104043
  • LCCN
    85121598
  • Country Code
    uk
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Cambridge ; New York, NY
  • Pages/Volumes
    lv, 237 p.
  • Size
    25 cm
  • Classification
  • Subject Headings
  • Parent Bibliography ID
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