Comments on "Stochastic choice of basis functions in adaptive function approximation and the functional-link net" [with 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/sub 0/, should be -w/sub 0//spl middot/y/sub 0/-u/sub 0/, where w/sub 0/=/spl alpha/w/spl circ//sub 0/; w/spl circ//sub 0/=(w/spl circ//sub 01/, /spl middot//spl middot//spl middot/, y/sub 0d/), and u/sub 0/ be independent and uniformly distributed in V/sup d/=[0; /spl Omega/]/spl times/[-/spl Omega/; /spl Omega/]/sup d-1/, I/sup d/, and [-2d/spl Omega/, 2d/spl Omega/], 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.