Geodesic
Applications of parabolic $B$-splines for solving interpolation problems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 23 (1983) no. 2, pp. 278-289

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The use of local basis functions ($B$-splines) in interpolation by parabolic splines is studied. Constraints on the mesh of interpolation nodes whereby diagonal dominance is ensured are obtained, and the limits of good stipulation of the matrix of the system of defining relations of the interpolation problem, are indicated. An expression is obtained for passing from one representation of a spline to another. Explicit expressions are obtained for constructing local approximation splines. It is shown that the latter have approximation properties similar to those of interpolation splines. 
@article{ZVMMF_1983_23_2_a3,
     author = {B. I. Kvasov},
     title = {Applications of parabolic $B$-splines for solving interpolation problems},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {278--289},
     publisher = {mathdoc},
     volume = {23},
     number = {2},
     year = {1983},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_1983_23_2_a3/}
}
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B. I. Kvasov. Applications of parabolic $B$-splines for solving interpolation problems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 23 (1983) no. 2, pp. 278-289. http://geodesic.mathdoc.fr/item/ZVMMF_1983_23_2_a3/