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

Abstract: 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, Frobenius formula, triangular factorization, general matrix inverse, least square method, innovation process, Kalman filter.

UDC: 517.925.54, 517.983.35

MSC: 15A06, 15A09, 11B37

Received August 22, 2018, published February 6, 2019

DOI: 10.33048/semi.2019.16.011

Bibliographic databases:

•