This article is cited in 1 paper

Orthogonal projectors and systems of linear algebraic equations

I. V. Kireev

Institute of Computational Modeling, Siberian Branch, Russian Academy of Sciences, Akademgorodok 50/44, Krasnoyarsk, 660036 Russia

Abstract: 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.

Key words: numerical methods, linear algebra, orthogonal projectors, Kaczmarz method, Krylov subspaces.

UDC: 519.6

Received: 19.02.2019
Revised: 31.01.2020
Accepted: 16.04.2020

DOI: 10.15372/SJNM20200306

 English version: Numerical Analysis and Applications, 2020, 13:3, 262–270

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