Geodesic
Orthogonal projectors and systems of linear algebraic equations
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 23 (2020) no. 3, pp. 315-324

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In this paper, an operator iterative procedure for constructing of the orthogonal projection of a vector on a given subspace is proposed. The algorithm is based on the Euclidean ortogonalization of power sequences of a special linear transformation generated by the original subspace. For consistent systems of linear algebraic equations, a numerical method based on this idea is proposed. Numerical results are presented. 
@article{SJVM_2020_23_3_a5,
     author = {I. V. Kireev},
     title = {Orthogonal projectors and systems of linear algebraic equations},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {315--324},
     publisher = {mathdoc},
     volume = {23},
     number = {3},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2020_23_3_a5/}
}
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I. V. Kireev. Orthogonal projectors and systems of linear algebraic equations. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 23 (2020) no. 3, pp. 315-324. http://geodesic.mathdoc.fr/item/SJVM_2020_23_3_a5/