Geodesic
Approximation by hyperbolic splines
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXI, Tome 472 (2018), pp. 179-194

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The paper considers the minimal hyperbolic splines and their properties. Formulas for constructing quadratic splines and the corresponding biorthogonal (dual) functionals are obtained. Numerical results, demonstrating how approximation quality can be improved by using hyperbolic splines and changing control parameters, are presented. 
@article{ZNSL_2018_472_a12,
     author = {E. K. Kulikov and A. A. Makarov},
     title = {Approximation by hyperbolic splines},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {179--194},
     publisher = {mathdoc},
     volume = {472},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2018_472_a12/}
}
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E. K. Kulikov; A. A. Makarov. Approximation by hyperbolic splines. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXI, Tome 472 (2018), pp. 179-194. http://geodesic.mathdoc.fr/item/ZNSL_2018_472_a12/