Hermite interpolation prescribes values and finitely many derivatives of a polynomial at distinct points.
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Hermite interpolation is a method of interpolating a set of data points that not only matches the function values (as in polynomial interpolation) but also matches the derivatives at those points. This is particularly useful when you have information about not just the values of a function at certain nodes but also the behavior of the function (i.e., its slope) at those nodes.