Methods for obtaining reliable solutions to systems of linear algebraic equations

Authors:
I. V. Sergienko;A. N. Khimich;M. F. Yakovlev
Affiliations:
V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine;V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine;V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine
Venue:
Cybernetics and Systems Analysis
Year:
2011

Citing 2
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Abstract

The general case of incompatible systems of linear algebraic equations with matrices of arbitrary rank is considered. The estimates for total errors are obtained for all the considered cases under conditions of approximate data. In solving systems by iterative methods, the conditions of completion of iterative processes that provide solutions with a prescribed accuracy are considered in detail. A special attention is given to the solution of incompatible systems with symmetric positive semidefinite matrices by the method of three-stage regularization in which an algorithm for choosing the regularization parameter is proposed that allows finding solutions with the required accuracy.