Neural network operators: Constructive interpolation of multivariate functions

@article{Costarelli2015NeuralNO,
  title={Neural network operators: Constructive interpolation of multivariate functions},
  author={Danilo Costarelli},
  journal={Neural networks : the official journal of the International Neural Network Society},
  year={2015},
  volume={67},
  pages={28-36}
}
In this paper, the interpolation of multivariate data by operators of the neural network type is proved. These operators can also be used to approximate continuous functions defined on a box-domain of R(d). In order to show this fact, a uniform approximation theorem with order is proved. The rate of approximation is expressed in terms of the modulus of continuity of the functions being approximated. The above interpolation neural network operators are activated by suitable linear combinations… CONTINUE READING