On Hermite-Birkhoff Interpolation

  • I. J. Schoenberg
Part of the Contemporary Mathematicians book series (CM)

Abstract

Let k and n be riatural numbers and let
$$ E = \left\| {{ \in _{ij}}} \right\|,\quad \left( {i = 1, \ldots k;j = 0,1, \ldots ,n - 1} \right), $$
be a matrix with k rows and n columns having elements
$$ { \in _{ij}} = 0\quad or\quad 1, $$
which are such that
$$ \sum\limits_{i,j} {{ \in _{ij}}} = n. $$
.

Keywords

Distinct Point Interpolation Problem Hermite Interpolation Hermite Type Taylor Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    G. D. Birkhoff. General mean value and remainder theorems with applications to mechanical differentiation and integration. Trans. Amer. Math. Soc. 7 (1906), 107–136.CrossRefGoogle Scholar
  2. 2.
    Ch. Hermite. Sur la formule d’interpolation de Lagrange. J. Reine Angeu. Math. 84 (1878), 70–79; Œuvres, Vol. 3, 432-443.CrossRefGoogle Scholar
  3. 3.
    J. H. Ahlberg and E. N. Nilson. The approximation of linear functionals. SIAM J. Numerical Anal., 3 (1966), 173–182.CrossRefGoogle Scholar
  4. 4.
    G. Polya. Bemerkungen zur Interpolation und zur Näherungstheorie der Balkenbiegung. Z. Angew. Math. Mech. 11 (1931), 445–449.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1988

Authors and Affiliations

  • I. J. Schoenberg
    • 1
  1. 1.Mathematics Research Center, U.S. Army, University of WisconsinMadisonUSA

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