@Article{JCM-1-317,
author = {Dong-Xu Qi and Shu-Zi Zhou},
title = {Local Explicit Many-Knot Spline Hermite Approximation Schemes},
journal = {Journal of Computational Mathematics},
year = {1983},
volume = {1},
number = {4},
pages = {317--321},
abstract = {<p style="text-align: justify;">If $f^{(i))}(\alpha)(\alpha=a, i=0,1,...,k-2)$ are given, then we get a class of the Hermite approximation operator Qf=F satisfying $F^{(i)}(\alpha)=f^{(i)}(\alpha)$, where F is the many-knot spline function whose knots are at points $y_i:$=$y_0$&lt;$y_1$&lt;$\cdots$&lt;$y_{k-1}=b$, and $F\in P_k$ on $[y_{i-1},y_i]$. The operator is of the form $Qf:=\sum\limits_{i=0}^{k-2}[f^{(i)}(a)\phi_i+f^{(i)}(b)\psi _i]$. We give an explicit representation of $\phi_i$ and $\psi_i$ in terms of B-splines $N_{i,k}$. We show that Q reproduces appropriate classes of polynomials.</p>},
issn = {1991-7139},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/jcm/9707.html}
}