Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-27T02:05:46.206Z Has data issue: false hasContentIssue false

Strongly and Weakly Non-Poised H-B Interpolation Problems

Published online by Cambridge University Press:  20 November 2018

R. Devore
Affiliation:
Oakland University, Rochester, Michigan
A. Meir
Affiliation:
Oakland University, Rochester, Michigan
A. Sharma
Affiliation:
University of Alberta, Edmonton, Alberta
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1973

References

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