تقرير
$L^{p}$-convergence of Kantorovich-type Max-Min Neural Network Operators
| العنوان: | $L^{p}$-convergence of Kantorovich-type Max-Min Neural Network Operators |
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| المؤلفون: | Aslan, İsmail, De Marchi, Stefano, Erb, Wolfgang |
| سنة النشر: | 2024 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Numerical Analysis, 41A30, 41A25 |
| الوصف: | In this work, we study the Kantorovich variant of max-min neural network operators, in which the operator kernel is defined in terms of sigmoidal functions. Our main aim is to demonstrate the $L^{p}$-convergence of these nonlinear operators for $1\leq p<\infty$, which makes it possible to obtain approximation results for functions that are not necessarily continuous. In addition, we will derive quantitative estimates for the rate of approximation in the $L^{p}$-norm. We will provide some explicit examples, studying the approximation of discontinuous functions with the max-min operator, and varying additionally the underlying sigmoidal function of the kernel. Further, we numerically compare the $L^{p}$-approximation error with the respective error of the Kantorovich variants of other popular neural network operators. As a final application, we show that the Kantorovich variant has advantages compared to the sampling variant of the max-min operator and Kantorovich variant of the max-product operator when it comes to approximate noisy functions as for instance biomedical ECG signals. Comment: 23 pages, 6 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2407.03329 |
| رقم الأكسشن: | edsarx.2407.03329 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |