  A novel type of approximants is introduced, being based on the ideas of
self-similar approximation theory. The method is illustrated by the examples
possessing the structure typical of many problems in applied mathematics. Good
numerical convergence is demonstrated for the cases that can be compared with
exact solutions, when these are available. The method is shown to be not less
and as a rule essentially more accurate than that of Pade approximants.
Comparison with other approximation methods is also given.
