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I've only seen the similiar problem but there are some entries on higher degree given.

Neuer
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1 Answers1

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No. It is impossible. Initial values $(x_i,f(x_i))$ are experimental data. You should measure them from real world phenomena or they should be given. Although you can approximate $f(x_2)$ by Newton forward difference formula using one of the pairs $\{(x_0,f(x_0)),(x_3,f(x_3))\}$, $\{(x_0,f(x_0)),(x_4,f(x_4))\}$, $\{(x_1,f(x_1)),(x_3,f(x_3))\}$ or $\{(x_1,f(x_1)),(x_4,f(x_4))\}$, but the result will not be the exact value of $f(x_2)$.

Dante
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