Vandermonde matrix

A Vandermonde matrixMathworldPlanetmath is any (n+1)×(n+1) matrix of the form


Vandermonde matrices usually arise when considering systems of polynomials evaluated at specific points (i.e. in interpolationMathworldPlanetmath or approximation). This may happen, for example, when trying to solve for constants from initial conditionsMathworldPlanetmath in systems of differential equations or recurrence relations.

Vandermonde matrices also appear in the computation of FFTs (Fast Fourier Transforms). Here the fact that Vandermonde systems Vz=b can be solved in 𝒪(nlogn) flops by taking advantage of their comes into play.

0.1 References

  1. 1.

    Golub and Van Loan, Matrix Computations, Johns Hopkins University Press 1993

Title Vandermonde matrix
Canonical name VandermondeMatrix
Date of creation 2013-03-22 13:04:19
Last modified on 2013-03-22 13:04:19
Owner akrowne (2)
Last modified by akrowne (2)
Numerical id 4
Author akrowne (2)
Entry type Definition
Classification msc 65T50
Classification msc 65F99
Classification msc 15A57