Orthogonal projectors and systems of linear algebraic equations
I.V. Kireev
Institute of computational modelling Siberian Branch of Russian Academy of Sciences, Krasnoyarsk, Rossia
Keywords: численные методы, линейная алгебра, ортогональные проекторы, метод Качмажа, подпространства Крылова, numerical methods, linear algebra, orthogonal projectors, Kaczmarz method, Krylov sub-spaces
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.
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