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Vandermonde interpolation approach (Definition)

The Vandermonde approach for interpolation is when we wish to determine the interpolating polynomial $ p(x)=a_0 + a_1x + a_2x^2 + \ldots +a_nx^n$ for the $ n+1$ points $ (x_i,y_i)$, $ i=0,1,\ldots, n$ by forming the equations $ y_i=a_0+a_1x_i+a_2x_2^2+\ldots+a_nx_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.

"Vandermonde interpolation approach" is owned by mathcam. [ full author list (2) | owner history (2) ]
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Cross-references: Vandermonde matrix, matrices, equations, points, polynomial, interpolation

This is version 5 of Vandermonde interpolation approach, born on 2004-04-24, modified 2005-03-17.
Object id is 5802, canonical name is VandermondeInterpolationApproach.
Accessed 1447 times total.

AMS MSC41A05 (Approximations and expansions :: Interpolation)
 65D05 (Numerical analysis :: Numerical approximation and computational geometry :: Interpolation)

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