Interpolation question

Question

I have a polynomial enter image description here such that

enter image description here

for i = 1, 2,..., N distinct nodes. How would I show that this possesses a unique solution and find a way of constructing it?

score 0 · Accepted Answer · answered Mar 14 '15 at 22:09

0

Construct the interpolation polynomial for the derivative values, integrate, adjust value at $x_0$ by the integration constant.

answered Mar 14 '15 at 22:09

Lutz Lehmann

Would this also show that the problem has a unique solution? – John Jay Mar 14 '15 at 22:18
Yes, since at its base the interpolation problem is a linear system of equations for the coefficients of the polynomial. $n+1$ equations for $n+1$ coefficients. Examine the kernel of this system. – Lutz Lehmann Mar 14 '15 at 22:25

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