Vozna S. Function Approximation by Continued Fractions and Two-dimensional Continued Fractions.

Interpolating formula in the form of an associated continued fraction and two-dimensional associated continued fraction of special type for one variable functions and for two variable functions have been constructed. The properties of a such associated continued fraction, obtained from interpolate formula have been investigated. Moreover the estimations of the approximating function by associated continued fraction have been obtained. The two-dimensional continued g-fraction is defined and the criteries of convergence of this fraction have been established. Truncation error bounds for two-dimensional continued g-fraction have been obtained.