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Strongly and Weakly Non-Poised H-B Interpolation Problems

  • R. Devore (a1), A. Meir (a1) and A. Sharma (a2)

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The problem of Hermite-Birkhoff interpolation is to determine: what n + 1 interpolatory conditions imposed on a polynomial P(x) of degree n and its derivatives determine the polynomial uniquely. It is customary now to indicate the imposed conditions by means of a matrix E = (eij) which is called the incidence matrix for the problem.

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References

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1. Atkinson, K. and Sharma, A., A partial characterization of poised Hermite-Birkhoff interpolation problems, SIAM J. Numer. Anal. 6 (1969), 230236.
2. Ferguson, D., The question of uniqueness for G. D. Birkhoff interpolation problems, J. Approximation Theory 2 (1969), 128.
3. Karlin, S. and Karon, J., On Hermite-Birkhoff interpolation (to appear).
4. Lorentz, G. G., Birkhoff interpolation and the problem of free matrices, J. Approximation Theory 6 (1972), 283290.
5. Lorentz, G. G. and Zeller, K., Birkhoff Interpolation, SIAM J. Numer. Anal. 8 (1971), 4348.
6. Sharma, A., Some poised and non-poised problems of interpolation, SIAM Rev. 14 (1972), 129151.
7. Szegö, G., Orthogonal polynomials, Amer. Math. Soc. Colloq. Pub. Vol. 23. (revised ed., 1958).
8. Tricomi, F., Vorlesungen über Orthogonalreihen (Springer-Verlag, Berlin, 1955).
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Strongly and Weakly Non-Poised H-B Interpolation Problems

  • R. Devore (a1), A. Meir (a1) and A. Sharma (a2)

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