Scattered data approximation by neural networks operators

In this paper, some feed-forward neural networks (FNNs) interpolation operators based on scattered data are introduced. Further, these operators are used as approximators to approximate bivariate continuous target function. By means of the translations and dilates of logistic function, some FNNs quasi-interpolation and exact interpolation operators are constructed, respectively. Using the modulus of continuity of function and the mesh norm of scattered data as measures, the corresponding approximation errors of the constructed operators are estimated. In addition, the well-known central B-splines are used to construct FNNs interpolation operators with compact support, and the corresponding approximation errors are also estimated.