A degree by degree recursive construction of Hermite spline interpolants

✍ Scribed by Xuli Han

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 853 KB
• Volume: 225
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/j.cam.2008.07.005

✦ Synopsis

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.