Lagrange polynomial

In numerical analysis, Lagrange polynomials are used for polynomial interpolation. For a given set of distinct points ${\displaystyle x_{j}}$ and numbers ${\displaystyle y_{j}}$, the Lagrange polynomial is the polynomial of lowest degree that assumes at each point ${\displaystyle x_{j}}$ the corresponding value ${\displaystyle y_{j}}$ (i.e. the functions coincide at each point). The interpolating polynomial of the least degree is unique, however, and since it can be arrived at through multiple methods, referring to "the Lagrange polynomial" is perhaps not as correct as referring to "the Lagrange form" of that unique polynomial.

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