Geodesic
On some applications of bilateral orthogonalization in computational algebra
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 187-205

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In this article it is proved that the equations of sequential solution of a number of computational algebra problems are the consequences of equations of counter orthogonalization and biorthogonalization in Hilbert and Euclidean spaces. The basis of these equations is the known sequential method of direct Gram–Sonin–Schmidt orthogonalization. It is considered the problems related to matrix inversions, their triangular factorizations, and solving systems of linear algebraic equations.
Keywords: Gram–Sonin–Schmidt orthogonalization, bilateral orthogonalization, triangular factorization, general matrix inverse, least square method, innovation process, Kalman filter.
Mots-clés : Frobenius formula 
@article{SEMR_2019_16_a82,
     author = {A. O. Egorshin},
     title = {On some applications of bilateral orthogonalization in computational algebra},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {187--205},
     publisher = {mathdoc},
     volume = {16},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2019_16_a82/}
}
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A. O. Egorshin. On some applications of bilateral orthogonalization in computational algebra. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 187-205. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a82/