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In numerical analysis, polynomial interpolation is the interpolation of a given data set by the polynomial of lowest possible degree that passes through the points of the dataset.
Given a set of n + 1 data points , … , {\displaystyle ,\ldots ,} , with no two x j {\displaystyle x_{j}} the same, a polynomial function p {\displaystyle p} is said to interpolate the data if p = y j {\displaystyle p=y_{j}} for each j ∈ { 0 , 1 , … , n } {\displaystyle j\in \{0,1,\dotsc ,n\}}.
Two common explicit formulas for this polynomial are the Lagrange polynomials and Newton polynomials.