Vandermonde Polynomial Interpolation
Interpolation Points
i
i
i
x
i
x_i
x
i
y
i
y_i
y
i
0
0
0
Remove
1
1
1
Remove
2
2
2
Remove
3
3
3
Remove
4
4
4
Remove
i
i
i
Add
Refresh
[
1
−
10
100
−
1000
10000
1
−
4
16
−
64
256
1
0
0
0
0
1
6
36
216
1296
1
10
100
1000
10000
]
−
1
⋅
[
−
5
9
−
5
7
−
8
]
=
[
−
5
−
1.1857142857142855
0.7409523809523809
0.01035714285714285
−
0.007559523809523809
]
\begin{bmatrix}1 & -10 & 100 & -1000 & 10000 \\ 1 & -4 & 16 & -64 & 256 \\ 1 & 0 & 0 & 0 & 0 \\ 1 & 6 & 36 & 216 & 1296 \\ 1 & 10 & 100 & 1000 & 10000\end{bmatrix}^{-1} \cdot{} \begin{bmatrix}-5\\9\\-5\\7\\-8\end{bmatrix} = \begin{bmatrix}-5\\-1.1857142857142855\\0.7409523809523809\\0.01035714285714285\\-0.007559523809523809\end{bmatrix}
1
1
1
1
1
−
10
−
4
0
6
10
100
16
0
36
100
−
1000
−
64
0
216
1000
10000
256
0
1296
10000
−
1
⋅
−
5
9
−
5
7
−
8
=
−
5
−
1.1857142857142855
0.7409523809523809
0.01035714285714285
−
0.007559523809523809
References:
Vandermonde matrix