Knot insertion and knot removal matrices for nonpolynomial splines
Numerical methods and programming, Tome 13 (2012) no. 1, pp. 74-86
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Continuously differentiable splines of second order on a nonuniform grid are constructed. Formulas of polynomial and nonpolynomial (trigonometric and hyperbolic) are given. Calibration relations expressing the coordinate splines on the original grid as a linear combination of splines of the same type on a refined grid and calibration relations representing the coordinate splines on an enlarged grid as a linear combination of splines of the same type on the original grid are obtained. Knot insertion and knot removal matrices on an interval and on a segment for splines associated with infinite and finite nonuniform grids respectively are constructed.
Keywords:
spline; wavelet; biorthogonal systems; decomposition matrix; reconstruction matrix; subdivision scheme; knot insertion and removal algorithms; spline curve.
@article{VMP_2012_13_1_a9,
author = {A. A. Makarov},
title = {Knot insertion and knot removal matrices for nonpolynomial splines},
journal = {Numerical methods and programming},
pages = {74--86},
publisher = {mathdoc},
volume = {13},
number = {1},
year = {2012},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VMP_2012_13_1_a9/}
}
A. A. Makarov. Knot insertion and knot removal matrices for nonpolynomial splines. Numerical methods and programming, Tome 13 (2012) no. 1, pp. 74-86. http://geodesic.mathdoc.fr/item/VMP_2012_13_1_a9/