What does POLYNOMIAL INTERPOLATION stand for? 

Polynomial interpolation

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 ( x 0 , y 0 ) , … , ( x n , y n ) {\displaystyle (x_{0},y_{0}),\ldots ,(x_{n},y_{n})} , with no two x j {\displaystyle x_{j}} the same, a polynomial function p ( x ) {\displaystyle p(x)} is said to interpolate the data if p ( x j ) = y j {\displaystyle p(x_{j})=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.

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