Lagrange polynomial

The Lagrange polynomial can also be computed in finite fields.

The resulting solution to the interpolation problem is called the Lagrange polynomial.

As can be seen in the following derivation the weights are derived from the Lagrange polynomials.

The set is another basis for quadratic polynomials, called the Lagrange polynomial.

In numerical analysis, Lagrange polynomials are used for polynomial interpolation.

Bicubic interpolation can be accomplished using either Lagrange polynomials, cubic splines, or cubic convolution algorithm.

Lagrange polynomials are used in the Newton-Cotes method of numerical integration and in Shamir's secret sharing scheme in cryptography.

The element consists of a combination of two sets of Lagrange polynomials, each one used to define the variation of a field in each orthogonal direction of the local referential.

The LPM uses Lagrange polynomials for the approximations, and Legendre-Gauss-Lobatto (LGL) points for the orthogonal collocation.

Another variant, called the Hermite-LGL method uses piecewise cubic polynomials rather than Lagrange polynomials, and collocates at a subset of the LGL points.

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).

In a somewhat opposite manner, the approximation for the costate (adjoint) is performed using a basis of Lagrange polynomials that includes the final value of the costate plus the costate at the N LG points.