Summary
A method for the construction of a set of data of interpolation in several variables is given. The resulting data, which are either function values or directional derivatives values, give rise to a space of polynomials, in such a way that unisolvence is guaranteed. The interpolating polynomial is calculated using a procedure which generalizes the Newton divided differences formula for a single variable.
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References
Chung, K.C., Yao, T.H.: On lattices admitting unique Lagrange interpolation. SIAM J. Num. Anal.14, 735–743 (1977)
Ciarlet, P.G., Raviart, P.A.: General Lagrange and Hermite interpolation inR n with applications to finite element methods. Arch. Rational Mech. Anal.46, 177–199 (1972)
Guenter, R.B., Roetman, E.L.: Some observations on interpolation in higher dimensions. Math. Comp.24, 517–521 (1970)
Maeztu, J.I.: Interpolation de Lagrangey Hermite enR k. Doctoral dissertation (in Spanish) directed by M. Gasca. University of Granada (1979)
Mitchell, A.R., Wait, R.: The finite element method in partial differential equations. New York: John Wiley & Sons 1977
Salzer, H.E.: Divided differences for functions of two variables for irregularly spaced arguments. Num. Math.6, 68–77 (1964)
Thacher, H.C. Jr.: Derivation of interpolation formulas in several independent variables. Ann. New York. Acad. Sci.86, 758–775 (1960)
Werner, H.: Remarks on Newton type multivariate interpolation for subsets of grids. Computing25, 181–191 (1980)
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Gasca, M., Maeztu, J.I. On Lagrange and Hermite interpolation in Rk . Numer. Math. 39, 1–14 (1982). https://doi.org/10.1007/BF01399308
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DOI: https://doi.org/10.1007/BF01399308