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

In the article, we propose an incremental algorithm for calculating the inversion of the confluent Vandermonde matrix and triangular factorization of this inversion. We implemented all the incremental operations, i.e. adding, deleting and changing the single matrix parameter to avoid repeating the same calculations again and again. Besides, contrary to other works in this field, the article derives an explicit analytic formula for the calculation of the triangular factorization of the confluent Vandermonde matrix inversion. Additionally, we propose a solution to these two problems with the use of a system of linear recursive equations. The results of this article do not require any symbolic calculations. Therefore they can be performed by a numerical algorithm implemented in any general-purpose programming language.