Geodesic
Smoothing by $L$-spline functions of many variables
Matematičeskie zametki, Tome 15 (1974) no. 3, pp. 371-379

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We investigate the problem of the smoothing of experimental data by cell-like $L$-spline functions of many variables from the point of view of the theory of such functions proposed by the author. Given values of a function and its derivatives up to some order are smoothed on a rectangular network of nodes. Existence and uniqueness of the solution are proved and equations are derived. 
@article{MZM_1974_15_3_a2,
     author = {Yu. S. Zav'yalov},
     title = {Smoothing by $L$-spline functions of many variables},
     journal = {Matemati\v{c}eskie zametki},
     pages = {371--379},
     publisher = {mathdoc},
     volume = {15},
     number = {3},
     year = {1974},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1974_15_3_a2/}
}
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Yu. S. Zav'yalov. Smoothing by $L$-spline functions of many variables. Matematičeskie zametki, Tome 15 (1974) no. 3, pp. 371-379. http://geodesic.mathdoc.fr/item/MZM_1974_15_3_a2/