If I use an interpolating polynomial to approximate the value of funcion $f$ at given $x$ and the polynomial is unique does it mean that the value of the polynomial is equal to the value of $f$ ($error = 0$) for evry $x$ in the function's domain? If so, then why?
2026-03-25 02:59:32.1774407572
Interpolating polynomial - relation between uniqueness and the error of approximation
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The answer is No. The value of the polynomial is equal to the value of $f$ only at the points of interpolating. See this link