Hey all, since I was programming a polynomial interpolater i found it easier to use the expanded divided difference $$ f[x_0 ,...,x_n] = \sum_{j=0}^{n} \frac{f(x_j)}{\Pi_{k}^{n,j \neq k} (x_j - x_k)} $$ , it works, but I can find no proof, any help/ references appreciated.(adsbygoogle = window.adsbygoogle || []).push({});

Second question: how accurate is Newton interpolating polynomial supposed to be? I gave it points from the function $$ -x^5 +x^4 +x^3 +x^2 +x+1 $$,

(1, 4), (2, -1),(3, -122),(4, -683),(5, -2344)

and it re-interpolated them correctly, but when I gave it the unknown point (6, -6221) it gave (6,-6101), is this error unnaturally large?

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# Proof of expanded divided difference?

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