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We study the enclosing problem for discrete and continuous dynamical systems in the context of computer assisted proofs. We review and compare the existing methods and emphasize the importance of developing a suitable set arithmetic for efficient algorithms solving the enclosing problem.
Stochastic arithmetic has been developed as a model for exact
computing with imprecise data. Stochastic arithmetic provides confidence
intervals for the numerical results and can be implemented in any existing
numerical software by redefining types of the variables and overloading the
operators on them. Here some properties of stochastic arithmetic are further
investigated and applied to the computation of inner products and the
solution to linear systems. Several numerical experiments are performed
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