Matrix expression of Hermite interpolation polynomials (Q1368454)

Matrix expression of the Hermite interpolation polynomials are constructed, in the form \(H(x)= \sum^n_{i=0} \sum^{d_i}_{k=0} h_{ik} (x){f^{(k)} (x_i) \over k!}\), satisfying the conditions \(H^{(\ell)} (x_j)= f^{(\ell)} (x_j)\), \(j=0, \dots,n\); \(\ell=0, \dots d_j\) where \(f\in C^d [a,b]\), \(a\leq x_0<x_1 \leq\dots \leq x_n\leq b\); \(d_0,d_1, \dots, d_n\) are nonnegative polynomials with degree at most \(m+ \sum^n_{i=0} d_i\). The author states that for construction of polynomials it is efficient to use a computer algebra system.