Vandermonde systems on equidistant nodes in [0, 1]: accurate computation

摘要

This paper deals with Vandermonde matrices V whose nodes are the equidistant points in [0, 1]. We give an analytic factorization and explicit formula for the entries of their inverse, and explore its computational issues. We also give asymptotic estimates of the Frobenius norm of both V and its inverse and show that a new representation of the floating point number system allows one to build an accurate algorithm for the interpolation problem on equidistant nodes in [0, 1].