Abstract
We consider a linear interval system with a regular n × n interval matrix [A] which has the form [A] = I + [-R,R]. For such a system we prove necessary and sufficient conditions for the applicability of the interval Gaussian algorithm where applicability means that the algorithm does not break down by dividing by an interval which contains zero. If this applicability is guaranteed we compare the output vector [x]G with the interval hull of the solution set \(S = \tilde x\left\{ {\left| {\exists \tilde A \in \left[ A \right]\tilde b \in \left[ b \right]} \right.:\tilde A\tilde x = \tilde b} \right\}\). In particular, we show that in each entry of [x]G at least one of the two bounds is optimal. Linear interval systems of the above-mentioned form arise when a given general system is preconditioned with the midpoint inverse of the underlying coefficient matrix.
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Mayer, G., Rohn, J. On the Applicability of the Interval Gaussian Algorithm. Reliable Computing 4, 205–222 (1998). https://doi.org/10.1023/A:1009997411503
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DOI: https://doi.org/10.1023/A:1009997411503