A degree by degree recursive construction of Hermite spline interpolants

Authors:
Xuli Han
Affiliations:
School of Mathematics and Computing Technology, Central South University, Changsha, 410083, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

Citing 9
Cited 3

On the multi-level splitting of finite element spaces

Numerische Mathematik
Hierarchical conforming finite element methods for the biharmonic equation

SIAM Journal on Numerical Analysis
Curves and surfaces for computer aided geometric design (3rd ed.): a practical guide

Curves and surfaces for computer aided geometric design (3rd ed.): a practical guide
C1-hierarchical bases

Journal of Computational and Applied Mathematics
Refinable spline functions and Hermite interpolation

Mathematical Methods for Curves and Surfaces
Multi-node higher order expansions of a function

Journal of Approximation Theory
Surface compression using a space of C1 cubic splines with a hierarchical basis

Computing - Geometric modelling dagstuhl 2002
Recursive computation of bivariate Hermite spline interpolants

Applied Numerical Mathematics
A recursive construction of Hermite spline interpolants and applications

Journal of Computational and Applied Mathematics

Error inequalities for quintic and biquintic discrete Hermite interpolation

Journal of Computational and Applied Mathematics
Stability and convergence of the two parameter cubic spline collocation method for delay differential equations

Computers & Mathematics with Applications
Error estimates for discrete spline interpolation: Quintic and biquintic splines

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	7.30

Visualization

Abstract

Based on the classical Hermite spline interpolant H"2"n"-"1, which is the piecewise interpolation polynomial of class C^n^-^1 and degree 2n-1, a piecewise interpolation polynomial H"2"n of degree 2n is given. The formulas for computing H"2"n by H"2"n"-"1 and computing H"2"n"+"1 by H"2"n 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"2"n satisfies the same interpolation conditions as the interpolant H"2"n"-"1, and is an optimal approximation of the interpolant H"2"n"+"1. Some interesting properties are also proved.