On the global approximation and interpolation of locally described real valued functions

摘要

An approach for approximation and interpolation of real valued functions is presented, which is based on generalized blending methods. The aim is to find a simple procedure for deriving a global description g of a concerned function f. We suppose that a set of local descriptions gv, 1 ≤ v ≤ n, of f is given. The global description g is intended to approximate f at least as well as the local descriptions gv do, and g is of a prescribed degree of smoothness. The obtained method is applicable for processing any kind of local descriptions; algebraic expressions can be used as well as non-algebraic descriptions, like neuronal networks or fuzzy controllers.