Approximation of functions of several variables by multidimensional S-fractions with independent variables

The paper deals with the problem of approximation of functions of several variables by branched continued fractions. We study the correspondence between formal multiple power series and the so-called multidimensional S-fraction with independent variables. As a result, the necessary and sufficient conditions for the expansion of the formal multiple power series into the corresponding multidimensional S-fraction with independent variables have been established. Several numerical experiments show the efficiency, power and feasibility of using the branched continued fractions in order to numerically approximate certain functions of several variables from their formal multiple power series.

Automated summary

The paper discusses the approximation of functions of several variables by branched continued fractions. It explores the correspondence between formal multiple power series and multidimensional S-fractions with independent variables, and establishes the necessary and sufficient conditions for such expansions. Numerical experiments demonstrate the efficiency and feasibility of using branched continued fractions to approximate functions of several variables from their formal multiple power series.