# 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 VandermondeInterpolationApproach 2013-03-22 14:19:56 2013-03-22 14:19:56 mathcam (2727) mathcam (2727) 8 mathcam (2727) Definition msc 65D05 msc 41A05