A Study on Vectorisation and Paralellisation of the Monotonicity Approach

Solving parametric interval linear systems is one of the fundamental problems of interval computations. When the solution of a parametric linear system is a monotone function of interval parameters, then an interval hull of the parametric solution set can be computed by solving at most 2n real systems. If only some of the elements of the solution are monotone functions of parameters, then a good quality interval enclosure of the solution set can be obtained. The monotonicity approach, however, suffers from poor performance when dealing with large scale problems. Therefore, in this paper an attempt is made to improve the efficiency of the monotonicity approach. Techniques such as vectorisation and parallelisation are used for this purpose. The proposed approach is verified using some illustrative examples from structural mechanics.

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