Geodesic
Best approximations of functions of several variables by sums of functions of fewer variables
Matematičeskie zametki, Tome 5 (1969) no. 2, pp. 217-226.

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The minimum of the mean-square deviation of approximations of functions of several independent variables by sums of functions of fewer variables in a multidimensional parallelepiped is investigated. The approximating function yielding the minimum mean-square deviation is obtained and this minimum deviation is calculated. 
@article{MZM_1969_5_2_a8,
     author = {V. M. Mordashev},
     title = {Best approximations of functions of several variables by sums of functions of fewer variables},
     journal = {Matemati\v{c}eskie zametki},
     pages = {217--226},
     publisher = {mathdoc},
     volume = {5},
     number = {2},
     year = {1969},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1969_5_2_a8/}
}
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V. M. Mordashev. Best approximations of functions of several variables by sums of functions of fewer variables. Matematičeskie zametki, Tome 5 (1969) no. 2, pp. 217-226. http://geodesic.mathdoc.fr/item/MZM_1969_5_2_a8/