Experiments on the evaluation of functional ranges using a random interval arithmetic

On Underestimating in Interval Computations

“…However, this is not a crucial disadvantage from the point of view of applications to random interval arithmetic, which is meant as a main field of application of the proposed underestimates. Stochastic estimates of ranges of function values in random interval arithmetic are obtained as random convex combinations of standard overestimates and pseudo underestimates obtained by inner interval arithmetic [1,12,13]. The underestimates proposed in the present paper either coincide with or outperform those of inner interval arithmetic; e.g.…”

“…Details of application of underestimates for the analysis of systems of interval linear equations may be found in [8]. Our interest in underestimating is motivated by further development of the recently proposed techniques called random interval arithmetic [1] and balanced random interval arithmetic [12,13], where the range of function values is estimated using random combinations of overestimates and pseudo underestimates obtained by so-called inner interval arithmetic. As it is shown in the example in the present paper, there are cases where inner interval arithmetic fails to produce underestimates.…”

TELEMAC: An efficient hydrodynamics suite for massively parallel architectures

“…Several methods and tools have been developed over the years to analyse round-off error propagation. These include direct analysis, inverse analysis [5], methods based on interval arithmetic [6] and randomised interval arithmetic [7]. Compared to other tools, the CADNA (Control of Accuracy and Debugging for Numerical Applications) library [8] appears less intrusive on the original code.…”