Recursive numerical recipes for the high efficient inversion of the confluent Vandermonde matrices

In the article, we propose a recursive algorithm for calculating the inversion of the confluent Vandermonde matrix. Besides, contrary to other works in this field, the article derives an explicit analytic formula for the calculation of the inverse of the confluent Vandermonde matrix. The results of this article do not require any symbolic calculations and therefore can be performed by a numerical algorithm implemented in any general-purpose programming language. Moreover, a ready-to-use C++ full implementation of the recursive algorithm is attached.