Polynomial interpolation in several variables
A survey is presented on multivariate polynomial interpolation, especially those which lead to the construction of the data points which allow unique interpolation for given interpolation spaces. Construction of sets of interpolation points, interpolation by tensor product, obtaining an interpolation space from regular grids, chosing nodes and space, and the construction of an interpolation space was described. Remainder formulas for polynomial interpolation give an explicit representation for the interpolation error. Multipoint Taylor expansions, Ciarlet's formula, Newton approach and its formula, Kergin interpolation, and the connection between polynomial interpolation and polynomial ideals were included. 115 references are given.
scientific article; zbMATH DE number 1419515