Comments on "Stochastic choice of basis functions in adaptive function approximation and the functional-link net" [and reply].

This paper includes some comments and amendments of the above-mentioned paper by Igelnik et al. (1995). Subsequently, Theorem 1 in the above-mentioned paper has been revised. The significant change of the original theorem is the space of the thresholds in the hidden layer. The revised theorem says that the thresholds of hidden b(0), should be -w(0).y(0)-u(0), where w(0)=alphaw;(0); w;(0)=(w; (01), ..., y(0d)), and u(0 ) be independent and uniformly distributed in V(d)=[0; Omega]x[-Omega; Omega](d-1), I(d), and [-2dOmega, 2dOmega], respectively. In reply, Igelnik et al. acknowledge that a factor of two was omitted in the statement of a trigonometric identity. However, the validity of the essential point of Theorem 1 is unaltered.