A degree by degree recursive construction of Hermite spline interpolants (Q1004005)

Let \(H_{2n-1}\) be the Hermite polynomial of degree \(2n-1\) that interpolates the values and the first \(n-1\) derivatives of a given function at the endpoints of an interval. A polynomial \(H_{2n}\) of degree \(2n\) is defined that satisfies the same interpolation conditions as \(H_{2n-1}\) and is the best \(L^2\)-approximant of \(H_{2n+1}\). The paper includes error estimates and a recursive computation of \(H_j\) for \(j\geq 2\).