A degree by degree recursive construction of Hermite spline interpolants

作者：Han Xuli^*

来源：Journal of Computational and Applied Mathematics, 2009, 225(1): 113-123.

DOI：10.1016/j.cam.2008.07.005

• Interpolation
• Hermite spline
• Decomposition

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.

• 出版日期2009-3-1
• 单位中南大学