Lagrange interpolation

Description

The Lagrange polynomial interpolation is a reformulation of the Newton polynomial interpolation where the divided differences are avoided, and the nthn^{th} degree interpolation can be represented as:

fn(x)=∑i=0nLi(x)f(xi)f_n(x) = \sum_{i = 0}^{n} L_i(x)f(x_i)

where:

Li(x)=∏j=0,i≠jnx−xjxi−xjL_i(x) = \prod_{j = 0, i \ne j}^{n} \dfrac{x - x_j}{x_i - x_j}

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