Abstract
In this paper we present the LU decomposition of a generalized interval matrix ${\bf{A}}$ under a modified interval arithmetic. This modified interval arithmetic is defined on generalized intervals and possesses group properties with respect to the addition and multiplication operations. These properties cause that the two computed generalized interval matrices ${\bf{L}}$ and ${\bf{U}}$ from the LU decomposition satisfy ${\bf{A}}={\bf{L}}{\bf{U}}$, with equality in modified interval arithmetic instead of the weaker inclusion in the classical interval arithmetic. Some applications of the new technique for solving interval linear systems are given and effectiveness of the new approach is investigated along some numerical tests.
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