Year: 1983
Journal of Computational Mathematics, Vol. 1 (1983), Iss. 4 : pp. 317–321
Abstract
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 $y_i:$=$y_0$<$y_1$<$\cdots$<$y_{k-1}=b$, 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/1983-JCM-9707
Journal of Computational Mathematics, Vol. 1 (1983), Iss. 4 : pp. 317–321
Published online: 1983-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 5