בניית פראקטלים: שימור חומרה וניתוח צמיחה

תקציר מקורי באנגליתarXiv:2505.06229v2 Announce Type: replace Abstract: This paper introduces the construction of fractal interpolation functions (FIFs), whose graphs are the attractors of an iterated function system (IFS). Integrating concepts from approximation theory, $\alpha$-fractal functions are constructed, employing shallow neural network operators. Based on the same methodology, we developed fractal interpolation functions using only discrete function values, unlike traditional methods that require each value of the target function. In order to preserve the smoothness of the target function, a method for constructing such FIFs is introduced, employing four-layered neural network operators, i.e., whenever $f \in C^{r}[a,b]$, the corresponding FIF $f^{\alpha} \in C^{r}[a,b]$. This work uses key approxi