Results concerning interval linear systems with multiple right-hand sides and the interval matrix equation AX=BAX=B

This note tries to study different solution sets of the interval linear matrix equation AX=B, where A is a known square interval matrix of dimension m×mm×m, B is a rectangular interval matrix of dimension m×nm×n, while the unknown matrix XX is also of dimension m×nm×n. Firstly, we show that Shary’s results for interval linear systems with a single right-hand side vector cannot be simply generalized to the case of interval linear systems of the form AX=B. Secondly, we give some analytical characterizations of the AE-solution sets of this interval matrix equation. We use a linear programming method in order to find the interval hull matrix. On the other hand, we propose the use of an interval Gaussian elimination to find an enclosure for the united solution set of this matrix equation, since the LU decomposition of A is needed only once. Numerical examples have also been given.