Geodesic
Natural interpolate splines
Matematičeskoe modelirovanie, Tome 6 (1994) no. 4, pp. 77-114.

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A new principle is proposed for interpolative splines construction when boundary conditions are not given. A simple algorithm for parabolic and cubic splines is found for free parameters calculation. Numerical examples are presented; they testify that the spline accuracy corresponds to theoretical predictions. Some recommendations are given for practical calculations. 
@article{MM_1994_6_4_a7,
     author = {N. N. Kalitkin and L. V. Kuzmina},
     title = {Natural interpolate splines},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {77--114},
     publisher = {mathdoc},
     volume = {6},
     number = {4},
     year = {1994},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_1994_6_4_a7/}
}
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N. N. Kalitkin; L. V. Kuzmina. Natural interpolate splines. Matematičeskoe modelirovanie, Tome 6 (1994) no. 4, pp. 77-114. http://geodesic.mathdoc.fr/item/MM_1994_6_4_a7/