Numerical recipes for the high efficient inverse of the confluent Vandermonde matrices

In this paper, we derive a numerical recipe for the calculation of the inversion of the confluent Vandermonde matrix. The main result of this article does not require any symbolic calculations and therefore can be performed by a numerical algorithm implemented either in any high level (like Matlab or Mathematica) or low level programming language (C/C++/Java/Pascal/Fortran, etc.). The computational complexity of the presented algorithm is of an O(N2) class being, by the linear term, better than the ordinary Gauss elimination method. Moreover, a ready to use C++ full implementation of the algorithm is attached.