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Interval Gauss-Seidel Method for Generalized Solution Sets to Interval Linear Systems

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Reliable Computing

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. 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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