On the interpolation in linear normed spaces using multiple nodes - Adrian Diaconu (Journal of numerical analysis and approximation theory, 2015)
In the papers [2], [3], [4], [6], [7] we indicated a method of extending the notion of interpolation polynomial for the case of a non-linear mapping \(f : X → Y\) where \(X\) and \(Y\) are linear spaces with special structures. This extension o¤ers the possibility to establish, in this general and abstract case as well, the main properties known in the case of the interpolation of real fonctions. To switch to the case using multiple nodes, case that compulsorily uses the notion of Fréchet differential of the ?rst order as well as of superiour orders, we will point out the de?nition and certain properties of these differentials. On this basis we can present the manner of building an abstract interpolation polynomial with multiple nodes.