发表机构
ma.iitr.ac.in（印度理工学院马德拉斯分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一类保持严格正函数的神经网络算子，证明其在连续函数空间上的正性、线性、有界性及紧致区间上的均匀收敛，并通过数值实验和调制信号去噪应用展示其有效性。
AI 中文摘要
本文介绍了一类保持函数性质的神经网络算子，旨在保持一个预先给定的严格正函数。我们研究了所提算子在连续函数空间上的逼近行为，并证明它们是正的、线性的、定义良好的且有界的。具体地，我们在紧致区间上证明了均匀收敛性，并利用连续模得到了逼近误差的定量估计。为支持理论分析，我们进行了若干数值实验，重点关注指数函数和对数函数的保持。这些例子展示了所提算子的良好性能，并与现有神经网络算子进行了比较。此外，我们提供了所提方法在调制信号去噪中的应用，证明了其实际相关性。
英文摘要
In this paper, we introduce a class of function-preserving neural network operators designed to preserve a prescribed strictly positive function. We examine the approximation behaviour of the proposed operators on the space of continuous functions and show that they are positive, linear, well-defined, and bounded. Specifically, we demonstrate uniform convergence on compact intervals and get quantitative estimates of the approximation error in terms of the modulus of continuity. To support the theoretical analysis, we present several numerical experiments focusing on the preservation of exponential and logarithmic functions. These examples show how well the proposed operators perform and compare them with existing neural network operators. Also, an application to denoising modulated signals is provided, demonstrating the practical relevance of the proposed approach.
Comments23 pages, 5 figures
