Abstract
We construct new multivariate polynomial interpolation schemes of Hermite type. The interpolant of a function is obtained by specifying suitable discrete differential conditions on the restrictions of the function to algebraic hypersurfaces. The least space of a finite-dimensional space of analytic functions plays an essential role in the definition of these differential conditions.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
1. Bojanov, B., Xu, Y: On polynomial interpolation of two variables. J. Approx. Theory 120, 267–282 (2003)
2. de Boor, C., Ron, A.: On multivariate polynomial interpolation. Constr. Approx. 6, 287–302 (1990)
3. de Boor, C., Ron, A.: Computational aspects of polynomial interpolation in several variables. Math. Comp. 58, 705–727 (1992)
4. de Boor, C., Ron, A.: The least solution for the polynomial interpolation problem. Math. Z. 210, 347–378 (1992)
5. Bos, L.: On certain configurations of points in \(\mathbf{R}^n\) which are unisolvent for polynomial interpolation. J. Approx. Theory 64, 271–280 (1991)
6. Bos, L., De Marchi, S.: Fekete points for bivariate polynomials restricted to y=xm. East J. Approx. 6, 189–200 (2000)
7. Hakopian, H.A., Khalaf, M.F.: On the poisedness of Bojanov-Xu interpolation. J. Approx. Theory 135, 176–202 (2005)
8. Hakopian, H.A., Khalaf, M.F.: On the poisedness of Bojanov-Xu interpolation. II. EastJ. Approx. 11, 187–220 (2005)
9. Lorentz, R.A.: Multivariate Birkhoff interpolation. Lecture Notes in Math. 1516, 1992
10. Lorentz, R.A.: Multivariate Hermite interpolation by algebraic polynomials: a survey.J. Comput. Appl. Math. 122, 167–201 (2000)
11. Milnor, J.: Singular points of complex hypersurfaces. (Annals of Math. Studies 61, Princeton: Princeton University Press 1968
12. Shabat, B.V.: Introduction to complex analysis. Part II. Functions of several variables. (Translations of Math. Monographs. 10) Providence, RI: American Mathematical Society 1992
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bos, L., Calvi, JP. Multipoint Taylor interpolation. Calcolo 45, 35–51 (2008). https://doi.org/10.1007/s10092-008-0142-7
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s10092-008-0142-7