Article collection "Mathematical Problems of Cybernetics" №5, Moscow, 1994
On the complexity of continuous functions approximate implementation by circuits and formulas in the polynomial and some other bases
The present article investigates the complexity of continuous functions approximate implementation by circuits and formulas in finite continuous bases: the polynomial, the piecewise polynomial and the bases with a continuum of constants. The formulas are here understood as circuits without branching of elements' outputs (while the circuit inputs may branch). For the bases above we obtain estimates of the ԑ-approximation complexity.
continuous real-valued functions of several variables, uniform metric, uniform approximation, modulus of continuity of k-th order on a given variable, Holder condition, Kolmogorov ԑ-entropy, schemes and formulas in continuous bases, non-branching programs, complexity of continuous functions implementation by schemes and formulas