Polynomial Interpolation

Updated 01 Oct 2026

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What it is
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  constructs a polynomial that passes exactly through supplied data points
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Uniqueness
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  for $n+1$ distinct abscissas, there is exactly one interpolating polynomial of degree at most $n$
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Error
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  under sufficient differentiability, $f(x)-P_n(x)=f^{(n+1)}(\xi)\prod_{i=0}^{n}(x-x_i)/(n+1)!$ .
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Distinguish from
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  Unavailable reference generally allows residuals instead of forcing an exact fit
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  evaluation outside the sampled interval is extrapolation and canb e especially unreliable
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Related
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Linked references 4