A degree by degree recursive construction of Hermite spline interpolants

Based on the classical Hermite spline interpolant H(2n-1), which is the piecewise interpolation polynomial of class C(n-1) and degree 2n - 1, a piecewise interpolation polynomial H(2n) of degree 2n is given. The formulas for computing H(2n) by H(2n-1) and computing H(2n+1) by H(2n) are shown. Thus a simple recursive method for the construction of the piecewise interpolation polynomial set {H(j)} is presented. The piecewise interpolation polynomial H(2n) satisfies the same interpolation conditions as the interpolant H(2n-1), and is an optimal approximation of the interpolant H(2n+1). Some interesting properties are also proved. (C) 2008 Elsevier B.V. All rights reserved.