Abstract
In the paper, we advance a numerical technique for enclosing generalized AE-solution sets to interval linear systems. The main result of the paper is an extension of the well-known interval Gauss-Seidel method to the problems of outer estimation of these generalized solution sets. We give a theoretical study of the new method, prove an optimality property for the generalized interval Gauss-Seidel iteration applied to the systems with the interval M-matrices.
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Shary, S. P.: Outer Estimation of Generalized Solution Sets to Interval Linear Systems, Reliable Computing 5 (3) (1999), pp. 323-336. Also published in: Csendes, T. (ed.), Developments in Reliable Computing, Kluwer Academic Publishers, Dordrecht, 1999.
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Shary, S.P. Interval Gauss-Seidel Method for Generalized Solution Sets to Interval Linear Systems. Reliable Computing 7, 141–155 (2001). https://doi.org/10.1023/A:1011422215157
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DOI: https://doi.org/10.1023/A:1011422215157