Common
Hermite interpolation
Polynomial interpolation using derivative values
Hermite interpolation
In numerical analysis, Hermite interpolation, named after Charles Hermite, generalizes polynomial interpolation, which includes Lagrange interpolation and Newton interpolation. Polynomial interpolation allows computing a polynomial of degree less than n that takes the same value at n given points as a given function. Instead, Hermite interpolation computes a polynomial of degree less than n such that the polynomial and its first few derivatives have the same values at m (fewer than n) given points as the given function and its first few derivatives at those points. The number of pieces of information, function values and derivative values, must add up to n. The resulting polynomial is commonly known as the Hermite interpolating polynomial or the Hermite interpolant. There are various methods for computing and formulating the Hermite interpolating polynomial. As Hermite interpolation generalizes Newton interpolation, both can be derived from the calculation of divided differences...
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