Stancu-Type Generalizations of Neural Network Operators with Perturbed Sampling Nodes

Abstract

In this paper, we introduce a Stancu-type generalization of multivariate neural network operators (NNOs) by incorporating two parameters that perturb the sampling nodes. The proposed operators extend the existing NNOs by allowing flexibility in the placement of sampling nodes. We establish the well-definedness and boundedness of the operators and prove uniform convergence on compact domains. Furthermore, quantitative error estimates are derived in terms of the modulus of continuity, leading to a convergence rate result. A perturbation theorem is also established, showing how the Stancu-type operators differ from the existing NNOs. Numerical experiments are presented to illustrate the influence of the Stancu parameters on the approximations and to validate the theoretical results. Finally, an application to ECG signal reconstruction is considered, demonstrating that the proposed operators effectively preserve the essential characteristics of the signal while providing accurate approximations.

arXiv comment19 Pages, 5 Figures