A new criterion to guarantee the feasibility of the interval Gaussian algorithm
SIAM Journal on Matrix Analysis and Applications
Inner and outer bounds for the solution set of parametric linear systems
Journal of Computational and Applied Mathematics - Special issue: Scientific computing, computer arithmetic, and validated numerics (SCAN 2004)
Approximating solutions of fully fuzzy linear systems: A financial case study
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
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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 mxm, B is a rectangular interval matrix of dimension mxn, while the unknown matrix X is also of dimension mxn. 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.