Geodesic
The Lagrange principle in the problem of optimal inversion of linear operators in finite-dimensional spaces with a priori information about its solution
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 9, pp. 1512-1523

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The problem of solving a system of linear algebraic equations is examined. An application of the Lagrange principle to the optimal recovery in this problem is described. New optimal methods that use available information about the errors in the data and a priori information about the solution are proposed for solving such systems. 
@article{ZVMMF_2007_47_9_a6,
     author = {A. V. Bayev},
     title = {The {Lagrange} principle in the problem of optimal inversion of linear operators in finite-dimensional spaces with a~priori information about its solution},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1512--1523},
     publisher = {mathdoc},
     volume = {47},
     number = {9},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_9_a6/}
}
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A. V. Bayev. The Lagrange principle in the problem of optimal inversion of linear operators in finite-dimensional spaces with a priori information about its solution. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 9, pp. 1512-1523. http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_9_a6/