Generalized Vandermonde's system and Lagrange's interpolation

TL;DR

This paper introduces explicit formulas and an efficient quadratic time algorithm for solving generalized Vandermonde systems, enabling the computation of Lagrange interpolation polynomials for given data points.

Contribution

It provides the first explicit formulas and a quadratic time algorithm for generalized Vandermonde systems, improving computational efficiency for interpolation problems.

Findings

Explicit formulas for generalized Vandermonde systems

Quadratic time algorithm for solving these systems

Efficient computation of Lagrange interpolation polynomials

Abstract

We give explicit formulas as well as a quadratic time algorithm to solve (so called) generalized Vandermonde's systems of p linear equations and n variables. It allows in particular to find all (so called Lagrange's) interpolation polynoms with degree n-1 taking given values in p distinct points.