Matrix expression of hermite interpolation polynomials

For distinct points x0, x1, …, xn in , a function f of Cd[a,b] and nonnegative integers d0, d1, …, dn ≤ d, the Hermite interpolation polynomial of f(x) in Lagrange type determined by the data {f(l)(xi)} (i = 0, 1, …, n, L = 0, 1, …, di) is the polynomial with degree m + n (m = ∑ni=0 di) which is expressed by the linear combination of these data with suitable coefficient polynomials being independent of f(x) [1–3]. In this note, a matrix expression of the Hermite interpolation polynomial is studied.