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Enclosures for the solution set of parametric interval linear systems

Hladík M.

International Journal of Applied Mathematics and Computer Science

2012

Vol. 22, no. 3

561-574

We investigate parametric interval linear systems of equations. The main result is a generalization of the Bauer-Skeel and the Hansen-Bliek-Rohn bounds for this case, comparing and refinement of both. We show that the latter bounds are not provable better, and that they are also sometimes too pessimistic. The presented form of both methods is suitable for combining them into one to get a more efficient algorithm. Some numerical experiments are carried out to illustrate performances of the methods.

Solution sets for systems of linear interval eguations

Kulpa Z., Rosłaniec K.

Computer Assisted Mechanics and Engineering Sciences

2000

Vol. 7, No. 4

625-639

The paper discusses various classes of solution sets for linear interval systems of equations, and their properties. Interval methods constitute an important mathematical and computational tool for modelling real-world systems (especially mechanical) with (bounded) uncertainties of parameters, and for controlling rounding errors in computations. They are in principle much simpler than general probabilistic or fuzzy set formulation, while in the same time they conform very well with many practical situations. Linear interval systems constitute an important subclass of such interval models, still in the process of continuous development. Two important problems in this area are discussed in more detail - the classification of so-called united solution sets, and the problem of overestimation of interval enclosures (in the context of linear systems of equations called also a matrix coefficient dependence problem).