Dictionary:Lagrange interpolation formula

(l∂ granj’) A method of calculating a polynomial for interpolating between a set of values which are not necessarily equally spaced.

$y_{1}=y\left(x_{1}\right),y_{2}=y\left(x_{2}\right),...,y_{n}=y\left(x_{n}\right);$

$y\left(x_{1}\right)=[{\frac {(x-x_{2})(x-x_{3})...(x-x_{n})}{(x_{1}-x_{2})...(x_{1}-x_{n})}}]y_{1}+[{\frac {(x-x_{1})(x-x_{3})...(x-x_{n})}{(x_{2}-x_{1})...(x_{2}-x_{n})}}]y_{2}+...+[{\frac {(x-x_{1})(x-x_{2})...(x-x_{n-1})}{(x_{n}-x_{2})...(x_{n}-x_{n-1})}}]y_{n}$

that is, in the factors multiplying y_k the factor (x–x_k) is omitted. Named for Joseph Louis Lagrange (1736–1813), French mathematician.