Improved Hermite multivariate polynomial interpolation

In this paper we give an algorithm with complexity O(mu² ) to solve Hermite multivariate polynomial interpolation with mu conditions on its Hasse derivatives. In the case of bivariate interpolation used to perform list-decoding on Reed-Solomon of length n and dimension k with multiplicity m on each point, it permits to obtain a complexity in O(n²m⁴) which does not depend on the rate k/n and better than previously known complexity in O( n² m⁵(n/k)^(1/2)). This algorithm can also be used for recent interpolation list-decoding with three and more variables. For interpolation on polynomial with n points and M variables with prescribed multiplication order m the general complexity of the algorithm is O(n²m^2M)