Sib. Èlektron. Mat. Izv., 2019, Volume 16, Pages 187–205
Differentical equations, dynamical systems and optimal control
On some applications of bilateral orthogonalization in computational algebra
A. O. Egorshin
Sobolev Institute of Mathematics,
4, pr. Koptyuga,
Novosibirsk, 630090, Russia
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.
Gram–Sonin–Schmidt orthogonalization, bilateral orthogonalization, Frobenius formula, triangular factorization, general matrix inverse, least square method, innovation process, Kalman filter.
PDF file (229 kB)
MSC: 15A06, 15A09, 11B37
Received August 22, 2018, published February 6, 2019
A. O. Egorshin, “On some applications of bilateral orthogonalization in computational algebra”, Sib. Èlektron. Mat. Izv., 16 (2019), 187–205
Citation in format AMSBIB
\paper On some applications of bilateral orthogonalization in computational algebra
\jour Sib. \`Elektron. Mat. Izv.
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