On Hermite-Birkhoff Interpolation

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


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
$$ \sum\limits_{i,j} {{ \in _{ij}}} = n. $$


Distinct Point Interpolation Problem Hermite Interpolation Hermite Type Taylor Problem 
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    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
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    Ch. Hermite. Sur la formule d’interpolation de Lagrange. J. Reine Angeu. Math. 84 (1878), 70–79; Œuvres, Vol. 3, 432-443.CrossRefGoogle Scholar
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    J. H. Ahlberg and E. N. Nilson. The approximation of linear functionals. SIAM J. Numerical Anal., 3 (1966), 173–182.CrossRefGoogle Scholar
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    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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