Geodesic
Construction of approximation functionals for minimal splines
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXIV, Tome 504 (2021), pp. 136-156

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The paper presents formulas for constructing quadratic minimal splines, which explicitly depend on components of the generating vector function. Formulas for various approximation functionals for minimal splines used as coefficients in local approximation schemes are obtained. Examples of special cases of approximation constructions, which have a quasi-interpolation character, are provided. Results of numerical experiments on approximation of a circular arc by minimal splines are considered. 
@article{ZNSL_2021_504_a7,
     author = {E. K. Kulikov and A. A. Makarov},
     title = {Construction of approximation functionals for minimal splines},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {136--156},
     publisher = {mathdoc},
     volume = {504},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2021_504_a7/}
}
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E. K. Kulikov; A. A. Makarov. Construction of approximation functionals for minimal splines. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXIV, Tome 504 (2021), pp. 136-156. http://geodesic.mathdoc.fr/item/ZNSL_2021_504_a7/