Lagrange Interpolation

Updated 01 Oct 2026

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What it is
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  expresses an interpolating polynomial as a weighted sum of baiss polynomilas.
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Formula
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  $P_n(x)=\sum_{i=0}^{n}y_iL_i(x)$ .
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  $L_i(x)=\prod_{j\ne i}(x-x_j)/(x_i-x_j)$ .
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Property
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  $L_i(x_j)$ equals $1$ when $i=j$ and $0$ otherwise, so $P_n(x_i)=y_i$ .
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Related
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  Newton Interpolation represents the same unique polynomial in a different bsis

Linked references 2