Inverse of the Vandermonde matrix with applications

Abstract

The inverse of the Vandermonde matrix is given in the form of the product U-of two triangular matrices by the display of generating formulas from which the elements of U-l and L- ' may be directly computed. From these, it is directly possible to gen-erate special formulas for the approximation of linear transforms such as integrals, in-terpolants, and derivates for a variety of functions that behave as P(x)f(x), where P(x) is a polynomial and f(x) is generally not a polynomial and may have localized singular-ities.