Birkhoff Interpolation

This reference book provides the main definitions, theorems and techniques in the theory of Birkhoff interpolation by polynomials.

G. G. Lorentz (Author), K. Jetter (Author), S. D. Riemenschneider (Author)

9780521104043, Cambridge University Press

Paperback / softback, published 19 March 2009

296 pages
22.9 x 15.2 x 1.6 cm, 0.44 kg

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.

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.

Subject Areas: Calculus & mathematical analysis [PBK]