Explicit algorithm to the inverse of Vandermonde Matrix

The Inverse matrix of Vandermonde Matrix has been considered to be one of the key components of symbolic computation. In this paper, based on the linear equations theory, a constructive proof of the Lagrange interpolation formula has been given. In the inference process, solving the inverse matrix of Vandermonde matrix is a key point. And then, using the generalized Yang Hui triangle theory, an explicit algorithm for the inverse matrix of Vandermonde matrix was given. Finally, experimental results indicate that this method is more effective than the function INV of MATLAB.