On solvability of interpolation problem for rational functions

Unlike the polynomial interpolation, where the solution exists, is unique, and can be written explicitly, the problem of rational interpolation may have no solution. The system of algebraic equations which we obtain may by arbitrary “bad”. The author [1] has developed the approach based on the algebra of rational functions which leads to the explicit solution without use of systems. This method allows us to describe the cases of solvability which have the spectral nature.