Stancu-Type Generalizations of Neural Network Operators with Perturbed Sampling Nodes
This work provides an incremental improvement for researchers in approximation theory and signal processing by enhancing flexibility in neural network-based operators.
The paper tackles the problem of improving neural network operators by introducing a Stancu-type generalization with parameters to perturb sampling nodes, resulting in proven uniform convergence and quantitative error estimates, with numerical experiments showing effective noise suppression in ECG signal denoising.
In this paper, we introduce a Stancu-type generalization of multivariate neural network operators by incorporating two parameters that perturb the sampling nodes. The proposed operators extend the existing neural network operator by allowing greater 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 convergence rate results. Numerical experiments are presented to illustrate the approximation behavior of the proposed operators and to demonstrate the effect of the Stancu parameters on the sampling nodes and the approximation accuracy. Finally, the application of signal denoising is demonstrated using a synthetic ECG signal, showing that the proposed operators effectively suppress noise while preserving the signal's main characteristics.