A Generalization of the Remainder in Multivariate Polynomial Interpolation (original) (raw)

The aim of this article is to introduce a generalization of the interpolation remainder in multivariate interpolation and to study it, in least interpolation schemes and in minimal interpolation ones. This generalization, we named λ-remainder, allows us a deeper analysis of the error in the interpolation process. Connected to the λ -remainder, we introduced the notion of λ -error order of interpolation. In the end we provide particular applications of the results we obtained. Interesting additionally theorems are also proved.