Vandermonde Polynomial Approximation

Approximation Points

iixix_iyiy_i
00
11
22
33
44
ii
([11111−10−4061010016036100−1000−6402161000]T[1−10100−10001−416−64100016362161101001000])−1[11111−10−4061010016036100−1000−6402161000]T⋅[−2−8−38−6]=[−1.05264868378290542.3934622467771645−0.026169970750731224−0.02584768714115481]\left(\begin{bmatrix}1 & 1 & 1 & 1 & 1 \\ -10 & -4 & 0 & 6 & 10 \\ 100 & 16 & 0 & 36 & 100 \\ -1000 & -64 & 0 & 216 & 1000\end{bmatrix}^T\begin{bmatrix}1 & -10 & 100 & -1000 \\ 1 & -4 & 16 & -64 \\ 1 & 0 & 0 & 0 \\ 1 & 6 & 36 & 216 \\ 1 & 10 & 100 & 1000\end{bmatrix}\right)^{-1} \begin{bmatrix}1 & 1 & 1 & 1 & 1 \\ -10 & -4 & 0 & 6 & 10 \\ 100 & 16 & 0 & 36 & 100 \\ -1000 & -64 & 0 & 216 & 1000\end{bmatrix}^T \cdot{} \begin{bmatrix}-2\\-8\\-3\\8\\-6\end{bmatrix} = \begin{bmatrix}-1.0526486837829054\\2.3934622467771645\\-0.026169970750731224\\-0.02584768714115481\end{bmatrix}

References: