Институт вычислительной математики
и математической геофизики

The International Conference on Computational Mathematics


Computational algebra

Investigation of Kaczmarz algorithm for solution of systems of linear algebraic equations

Makhotkin O.A.

Institute of Computational Mathematics and MG SB RAS (Novosibirsk)

In 1937 year S.Kaczmarz has proposed the iteration method for solution of systems of linear equations. In this method the solution is found by sequential orthogonal projection of approximation vector on hypersurfaces, connected with rows of considerd system. The method converges for any nonsingular matrix.

The results of computer experiments are presented for the standard method and its modifications. The estimations of complexity of iteration methods and there satisfiability for solution of practical problems are also presented.

Note. Abstracts are published in author's edition

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