Abstract
The paper generalizes the concept of “solving a system of linear algebraic equations in order to formulate a unified approach to the analysis of incompatible, indefinite and unstable systems”. Examples of unstable systems of linear algebraic equations are considered, which solutions depend on small changes in the numerical coefficients in the equations. The reasons for the instability of linear systems and the regularization algorithm for finding the solution of any system of linear algebraic equations are discussed. As the author notes, the Tikhonov regulatory algorithm is the most popular and practically convenient for solving unstable SLAES.
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