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  5. Solution of direct and inverse problem for a system of linear algebraic equations with interval-given characteristics

Solution of direct and inverse problem for a system of linear algebraic equations with interval-given characteristics

V.Yu. Dubnitskiy, A.M. Kobylin
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Direct and inverse problem was set for a system of linear algebraic equations wherein all forming elements were given in interval form. It was shown that the result of inverse problem solution might be used for synthesis of linear systems under known effects on them and their responses to such effects. Algorithms were proposed for direct and inverse problem solution united by a common methodological technique which consists in coming of direct and inverse solution to solution of a multi-criterion optimization problem. For its solution we used a search method based on choice of the best solution 0n the basis of a method connected with use of almost uniform sequences.
Keywords: systems of linear algebraic equations, direct problem solution of a system of linear algebraic equations, inverse problem solution of a system of linear algebraic equations, interval analysis, almost uniformly distributed sequences, nonstandard interval analysis, measurement indeterminacy