Chebyshev approximation by discrete superposition. Application to neural networks (Q1923884)

The author gives two algorithms for Chebyshev approximation of continuous functions on \([0,1]^n\). The two algorithms are based on the superposition theorem of \textit{A. N. Kolmogorov} [Trans., II. Ser., Am. Math. Soc. 28, 55-59 (1963); translation from Dokl. Akad. Nauk SSSR 114, 953-956 (1957; Zbl 0125.30803)] and both differ in the construction of the approximating function. Also, the author gives an error bound and extends a result of \textit{V. Kurkova} [Kolmogorov's theorem and multilayer neural networks, Neural Networks 5, 501-506 (1992)].