Vandermonde interpolation approach

The Vandermonde approach for interpolation is when we wish to determine the interpolating polynomial $p(x)=a_{0}+a_{1}x+a_{2}x^{2}+\ldots+a_{n}x^{n}$ for the $n+1$ points $(x_{i},y_{i})$ , $i=0,1,\ldots,n$ by forming the equations $y_{i}=a_{0}+a_{1}x_{i}+a_{2}x_{2}^{2}+\ldots+a_{n}x_{n}^{n}$ for $i=0,1,\ldots,n$ , and solving for the unknown coefficients $a_{0},a_{1},\ldots,a_{n}$ .

The system of equations can be written by using matrices $Y=XA$ where $X$ is a Vandermonde matrix.

Title	Vandermonde interpolation approach
Canonical name	VandermondeInterpolationApproach
Date of creation	2013-03-22 14:19:56
Last modified on	2013-03-22 14:19:56
Owner	mathcam (2727)
Last modified by	mathcam (2727)
Numerical id	8
Author	mathcam (2727)
Entry type	Definition
Classification	msc 65D05
Classification	msc 41A05