Interval approximation of higher order to the ranges of functions
Some of the results obtained earlier by the authors are now generalized and extended to higher-order approximations for multivariate polynomials and functions. First the Bernstein and the \(B\)-spline forms of multivariate polynomials are described. Next, a multivariate Taylor formula is derived. In the final section these results are combined in an effective approximation method of higher order to the range of functions. Due to the extensive computations an implementation on a computer is recommended. Examples are not presented.
scientific article; zbMATH DE number 880531