在数值分析中，拉格朗日插值法是以法国18世纪数学家约瑟夫·拉格朗日命名的一种多项式插值方法。许多实际问题中都用函数来表示某种内在联系或规律，而不少函数都只能通过实验和观测来了解。如对实践中的某个物理量进行观测，在若干个不同的地方得到相应的观测值，拉格朗日插值法可以找到一个多项式，其恰好在各个观测的点取到观测到的值。这样的多项式称为拉格朗日（插值）多项式。数学上来说，拉格朗日插值法可以给出一个恰好穿过二维平面上若干个已知点的多项式函数。拉格朗日插值法最早被英国数学家爱德华·华林于1779年发现，不久后（1783年）由莱昂哈德·欧拉再次发现。1795年，拉格朗日在其著作《师范学校数学基础教程》中发表了这个插值方法，从此他的名字就和这个方法联系在一起。

In numerical analysis, Lagrange polynomials are used for polynomial interpolation. For a given set of distinct points and numbers , the Lagrange polynomial is the polynomial of the least degree that at each point assumes the corresponding value (i.e. the functions coincide at each point). The interpolating polynomial of the least degree is unique, however, and it is therefore more appropriate to speak of "the Lagrange form" of that unique polynomial rather than "the Lagrange interpolation polynomial", since the same polynomial can be arrived at through multiple methods. Although named after Joseph Louis Lagrange, who published it in 1795, it was first discovered in 1779 by Edward Waring and it is also an easy consequence of a formula published in 1783 by Leonhard Euler.