INTERVAL GAUSSIAN ELIMINATION WITH PIVOT TIGHTENING∗

We present a method by which the breakdown of the interval Gaussian elimination caused by division of an interval containing zero can be avoided for some classes of matrices. These include the inverse nonnegative matrices, the totally nonnegative matrices, and the inverse M -matrices—all classes with identically signed inverses. The approach consists of a tightening of the interval pivot by determining the exact range of the pivot over the matrix interval.

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