Geodesic
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/}
}
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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/